{"id":81983,"date":"2020-12-17T11:17:55","date_gmt":"2020-12-17T10:17:55","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=81983"},"modified":"2023-09-15T13:21:45","modified_gmt":"2023-09-15T12:21:45","slug":"cours-en-ligne-loi-binomiale-terminale","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/","title":{"rendered":"Cours sur la loi binomiale en Terminale"},"content":{"rendered":"<div class=\"Latex_page\">\n<section class=\"has_ae_slider elementor-element elementor-section-full_width elementor-reverse-mobile elementor-section-stretched elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default elementor-section elementor-top-section\">\n<div class=\"elementor-container elementor-column-gap-no\">\n<div class=\"elementor-row\">\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\n\t\t<div data-elementor-type=\"page\" data-elementor-id=\"85134\" class=\"elementor elementor-85134\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-10da350a elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"10da350a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4b0929de sticky_badeau_colone strick_col ae-bg-gallery-type-default\" data-id=\"4b0929de\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-68eecbf elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"68eecbf\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3c6e4a1c strick_col ae-bg-gallery-type-default\" data-id=\"3c6e4a1c\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5e2a6b8d elementor-widget elementor-widget-heading\" data-id=\"5e2a6b8d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-terminale-maths\/\">Cours en ligne Maths en Terminale<\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b2d17b9 elementor-widget elementor-widget-heading\" data-id=\"b2d17b9\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p class=\"elementor-heading-title elementor-size-default\">Chapitres Maths en Terminale G\u00e9n\u00e9rale<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4afe09ff elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4afe09ff\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-recurrence-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Raisonnement et r\u00e9currence<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16c8edd8 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"16c8edd8\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-suites-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Les suites<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3bb57f03 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3bb57f03\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-limites-fonctions-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Les limites<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7b9945a3 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"7b9945a3\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-continuite-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Continuit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-752f886a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"752f886a\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-algorithmique-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Algorithmique<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1446b89c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"1446b89c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonction-exponentielle\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Fonctions exponentielles<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-53f6eff0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"53f6eff0\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonction-logarithme-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Fonctions logarithmes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6c1ead01 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6c1ead01\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonctions-trigonometriques-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Fonctions trigonom\u00e9triques<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2da72d22 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2da72d22\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-conditionnement-independance-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Conditionnement et ind\u00e9pendance<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1bb2d47c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"1bb2d47c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-primitives-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Primitives<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2c52a6c9 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2c52a6c9\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-derivees-convexite-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9rivation et convexit\u00e9<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4f5a8891 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4f5a8891\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-integration-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Calcul int\u00e9gral<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5aaddce0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5aaddce0\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-geometrie-dans-espace-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Figures et \u00e9quation cart\u00e9sienne<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-35f6fc16 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"35f6fc16\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9nombrement<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21b103a7 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"21b103a7\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Loi binomiale<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25ac19ad elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"25ac19ad\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-loi-grands-nombres-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Lois des grands nombres<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-84d8e42 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"84d8e42\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-normale-fluctuation-estimation\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Loi normale, intervalles, estimation<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3a67a9f5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3a67a9f5\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-nombres-complexes-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Nombres complexes - alg\u00e8bre<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1f63f3f6 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"1f63f3f6\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-polynomes-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">\u00c9quations polynomiales<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-17f1c156 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"17f1c156\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-complexes-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">G\u00e9om\u00e9trie et complexes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d329f92 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4d329f92\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-arithmetique-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Arithm\u00e9tique - Congruences<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fbdca41 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"fbdca41\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pgcd-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Arithm\u00e9tique - PGCD PPCM<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8ef8cbc elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8ef8cbc\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-nombres-premiers-fermat-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Nombres Premiers et Fermat<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1e7274d4 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"1e7274d4\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-matrices-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Matrices<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d362186 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"d362186\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-graphes-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Graphes<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e9acc30 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"e9acc30\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-chaine-markov-terminale\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Cha\u00eene de Markov<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49866b96 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"49866b96\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/nous-contacter\/\" class=\"elementor-button-link elementor-button elementor-size-sm\" role=\"button\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">CONTACTEZ-NOUS<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\n<\/div>\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\">\n<div class=\"style_pag\" style=\"color: #000;font-family: 'Lato', Sans-serif\">\n<div class=\"elementor-text-editor elementor-clearfix\">\n<h1 class=\"Latex_page_title\">La loi binomiale en Terminale G\u00e9n\u00e9rale<\/h1>\n<\/div>\n<p class=\"colone_latex_ancres\" style=\"text-align: center\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-loi-binomiale-terminale\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"text-align: center\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-terminale-maths\/\">Cours en ligne de Maths en Terminale<\/a><\/p>\n<h2>A. \u00c9preuves ind\u00e9pendantes en Terminale<\/h2>\n<h3><b>1. D\u00e9finition des \u00e9preuves ind\u00e9pendantes en Terminale<\/b><\/h3>\n<p>Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e7d9750ef16217fec27533b7016511c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#92;&#105;&#110;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"45\" style=\"vertical-align: -1px;\"\/>, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2e8c02acf1935830dc078ae9e9cbfc7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#92;&#103;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: -3px;\"\/>.<\/p>\n<p>Soient <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> \u00e9preuves <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a6a5211838ae8af7e27967dad72f586d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#69;&#125;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -3px;\"\/> pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-05c5dbcf347e53340bf3127b6763ba0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#49;&#44;&#92;&#44;&#32;&#110;&#093;&#92;&#33;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p>On note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-75390f77e60fe55929cd07cb9a8f28e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#79;&#109;&#101;&#103;&#97;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"\/> l&rsquo;univers (suppos\u00e9 fini) des r\u00e9sultats \u00e9l\u00e9mentaires associ\u00e9s \u00e0 l&rsquo;\u00e9preuve <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a6a5211838ae8af7e27967dad72f586d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#69;&#125;&#95;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -3px;\"\/>\u00a0 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-497225d6738cd17cfd2d6f3c024079d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: 0px;\"\/> la probabilit\u00e9 asso- ci\u00e9e.<\/p>\n<p>On note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-94374307f798b89549c5674f4a68f0aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#79;&#109;&#101;&#103;&#97;&#32;&#61;&#32;&#92;&#79;&#109;&#101;&#103;&#97;&#95;&#49;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#44;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#32;&#92;&#79;&#109;&#101;&#103;&#97;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"145\" style=\"vertical-align: -3px;\"\/> l&rsquo;univers associ\u00e9 \u00e0 l&rsquo;\u00e9preuve <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-fb1e11e13c33c9d9ad92194939f45f74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"\/> form\u00e9e par la succession des \u00e9preuves <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e7684489a5e6c533907290b93ebe08a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#69;&#125;&#95;&#49;&#92;&#44;&#32;&#44;&#32;&#92;&#44;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#44;&#44;&#92;&#44;&#32;&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#69;&#125;&#95;&#110;&#32;&#92;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\"\/>.<\/p>\n<p>Les<i>\u00a0\u00e9preuves<\/i>\u00a0sont\u00a0<i>ind\u00e9pendantes<\/i>\u00a0ssi la probabilit\u00e9 associ\u00e9e \u00e0 l&rsquo;\u00e9preuve <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-fb1e11e13c33c9d9ad92194939f45f74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#69;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"\/> v\u00e9rifie<br \/>\npour tout <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-05c5dbcf347e53340bf3127b6763ba0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#49;&#44;&#92;&#44;&#32;&#110;&#093;&#92;&#33;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -5px;\"\/>, et tout <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8257bbfabf7ab1e94dc2e75052281499_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#95;&#105;&#32;&#92;&#105;&#110;&#32;&#92;&#79;&#109;&#101;&#103;&#97;&#95;&#105;&#92;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -3px;\"\/>,<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e8ebc7a62dd3d712f624b9edf7d38cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#92;&#123;&#32;&#40;&#120;&#95;&#49;&#92;&#44;&#44;&#92;&#44;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#44;&#44;&#92;&#44;&#32;&#120;&#95;&#110;&#41;&#92;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#32;&#41;&#32;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10a1238e3d835e9db7376f38a58ac91a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#32;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#92;&#123;&#32;&#120;&#95;&#49;&#92;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#92;&#123;&#32;&#120;&#95;&#110;&#92;&#125;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#32;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"191\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p>Dans ce cas, si pour tout <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-05c5dbcf347e53340bf3127b6763ba0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#49;&#44;&#92;&#44;&#32;&#110;&#093;&#92;&#33;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"70\" style=\"vertical-align: -5px;\"\/>, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-449dff0152f224e70492870766d0b911_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;&#95;&#105;&#32;&#92;&#115;&#117;&#98;&#115;&#101;&#116;&#32;&#92;&#79;&#109;&#101;&#103;&#97;&#95;&#105;&#92;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"60\" style=\"vertical-align: -3px;\"\/>,<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6ba46abac851e1463397535da198287d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#65;&#95;&#49;&#92;&#44;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#44;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#44;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#44;&#32;&#65;&#95;&#110;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#32;&#41;&#32;&#61;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-85ff092707f25104d17ac4a5c56ca33a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#65;&#95;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#92;&#108;&#101;&#102;&#116;&#32;&#40;&#65;&#95;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#32;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"161\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p>N&rsquo;h\u00e9sitez pas \u00e0 prendre des <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">cours particuliers de maths<\/a> en cas de difficult\u00e9 lors de ce chapitre.<\/p>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"186412\" class=\"elementor elementor-186412\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-7b286009 elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"7b286009\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-64f5fda0 ae-bg-gallery-type-default\" data-id=\"64f5fda0\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bccc2bf elementor-widget elementor-widget-heading\" data-id=\"bccc2bf\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">COURS DE MATHS A DOMICILE<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ba807dc elementor-widget elementor-widget-heading\" data-id=\"6ba807dc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les meilleurs profs de maths pour <br\/> r\u00e9ussir sa scolarit\u00e9 <\/b><\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9f19bd5 elementor-widget elementor-widget-heading\" data-id=\"9f19bd5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">En ligne ou \u00e0 domicile<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2d959d5a elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"2d959d5a\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Je recherche un prof de maths \u00e0 domicile<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21d714d4 elementor-widget elementor-widget-text-editor\" data-id=\"21d714d4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left;\"><b>Avis Google France <\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-2ffb5a60 ae-bg-gallery-type-default\" data-id=\"2ffb5a60\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h3><b>2. Exemples d&rsquo;\u00e9preuves ind\u00e9pendantes <\/b><\/h3>\n<ul>\n<li>Les \u00e9preuves \u00ab\u00a0jeter un d\u00e9\u00a0\u00bb puis \u00ab\u00a0tirer une boule dans une urne\u00a0\u00bb sont des \u00e9preuves <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-conditionnement-independance-terminale\/\">ind\u00e9pendantes<\/a>.<\/li>\n<\/ul>\n<ul>\n<li>Les \u00e9preuves \u00ab\u00a0jeter un d\u00e9\u00a0\u00bb puis tirer une boule dans une urne portant le num\u00e9ro donn\u00e9 par le d\u00e9\u00a0\u00bb ne sont pas des \u00e9preuves ind\u00e9pendantes (sauf si les urnes ont la m\u00eame composition ! ).<\/li>\n<\/ul>\n<ul>\n<li>Les \u00e9preuves \u00ab\u00a0jeter <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> fois un d\u00e9\u00a0\u00bb sont ind\u00e9pendantes.<\/li>\n<\/ul>\n<ul>\n<li>Les \u00e9preuves \u00ab\u00a0tirer <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> fois une boule dans une urne\u00a0\u00bb<br \/>\n&#8230; sont ind\u00e9pendantes lorsque l&rsquo;on remet la boule \u00e0 l&rsquo;issue de chaque tirage<br \/>\n&#8230; ne sont pas ind\u00e9pendantes si la boule n&rsquo;est pas remise apr\u00e8s chaque tirage.<\/li>\n<\/ul>\n<h3><b>3. Utilisation d&rsquo;un arbre <\/b><\/h3>\n<p>On peut lorsque le nombre d&rsquo;\u00e9preuves <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> est faible et le nombre de r\u00e9sultats possibles \u00e0 chaque \u00e9preuve est faible, s&rsquo;aider d&rsquo;un arbre de probabilit\u00e9.<\/p>\n<h2><strong>B. Sch\u00e9ma de Bernoulli en Terminale<\/strong><\/h2>\n<h3><b>1. \u00c9preuve de Bernoulli en Terminale<\/b><\/h3>\n<p>On dit qu&rsquo;une \u00e9preuve est une\u00a0<i>\u00e9preuve de Bernoulli\u00a0<\/i>lorsqu&rsquo;elle m\u00e8ne \u00e0 la r\u00e9alisation de deux \u00e9v\u00e9nements <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-520cb534cd5b6bed768a61515b57cb7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>(appel\u00e9 succ\u00e8s) et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a56291ba5e2129c9852a27f44643ff3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#83;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"12\" style=\"vertical-align: 0px;\"\/> (appel\u00e9 \u00e9chec).<\/p>\n<h3><b>2. Variable al\u00e9atoire de Bernoulli en Terminale<\/b><\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/>\u00a0\u00c0 une \u00e9preuve de Bernoulli, on peut associer la <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-loi-grands-nombres-terminale\/\">variable al\u00e9atoire<\/a> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> d\u00e9finie par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7f586b92c4dedebd9042598a104ba3d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#32;&#61;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"\/> si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-520cb534cd5b6bed768a61515b57cb7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> est r\u00e9alis\u00e9 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-993c7c0aa11080ca552c4fededbcfe76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#32;&#61;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\"\/> si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-520cb534cd5b6bed768a61515b57cb7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/> n&rsquo;est pas r\u00e9alis\u00e9.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> On note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7a4b4e4095b79471109c049d2b3ad0b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#61;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#83;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"\/>, alors la loi de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> est donn\u00e9e par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b2e7e6b1eff2d61f0d6a94025912102f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#40;&#92;&#79;&#109;&#101;&#103;&#97;&#41;&#32;&#61;&#92;&#123;&#48;&#44;&#92;&#44;&#49;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d98f0a4e7ba5076dd91c191ffbb92233_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#61;&#32;&#49;&#41;&#32;&#61;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a3d7fa3b58d057b3081b5aae5e8f1124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#61;&#32;&#48;&#41;&#32;&#61;&#32;&#49;&#32;&#45;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p>On dit que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> suit\u00a0<i>une loi de Bernoulli de param\u00e8tre\u00a0<\/i><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/> et on note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-47f5f6c1f75ca0a8b6cd164f6cdb7a22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#32;&#92;&#104;&#111;&#111;&#107;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#66;&#125;&#40;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> R\u00e9ciproquement, si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> est une variable al\u00e9atoire dont la loi est d\u00e9finie par <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3ef88f1d05a98f309c00e258a97d03e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#40;&#92;&#79;&#109;&#101;&#103;&#97;&#41;&#32;&#61;&#32;&#92;&#123;&#48;&#32;&#44;&#92;&#44;&#32;&#49;&#92;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d98f0a4e7ba5076dd91c191ffbb92233_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#61;&#32;&#49;&#41;&#32;&#61;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a3d7fa3b58d057b3081b5aae5e8f1124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#61;&#32;&#48;&#41;&#32;&#61;&#32;&#49;&#32;&#45;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"\/>, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> est la variable al\u00e9atoire de Bernoulli associ\u00e9e \u00e0 l&rsquo;\u00e9preuve de Bernoulli telle que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0b6ff4f7479b6f586bf8e5ba64b9592f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#83;&#32;&#61;&#32;&#40;&#88;&#32;&#61;&#32;&#49;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0419c0679796575f9f9ad50a0c261730_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#32;&#123;&#83;&#125;&#32;&#61;&#32;&#40;&#88;&#32;&#61;&#32;&#48;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"97\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-47f5f6c1f75ca0a8b6cd164f6cdb7a22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#32;&#92;&#104;&#111;&#111;&#107;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#66;&#125;&#40;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\"\/>,<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c7f559dfe1cd1953f0c01eeb52f2b296_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#114;&#109;&#123;&#69;&#125;&#40;&#88;&#41;&#32;&#61;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-793ddd35ae4ca4ffff7e7b2b874e49b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#114;&#109;&#123;&#86;&#125;&#40;&#88;&#41;&#32;&#61;&#32;&#112;&#40;&#49;&#32;&#45;&#32;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<h3><b>3. Sch\u00e9ma de Bernoulli<\/b><\/h3>\n<p>Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-90dfe4768bfa5842274340262040a00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#92;&#105;&#110;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#78;&#125;&#94;&#42;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"51\" style=\"vertical-align: -1px;\"\/>, on dit que l&rsquo;on a un\u00a0<i>sch\u00e9ma de Bernoulli\u00a0<\/i>lorsque l&rsquo;on r\u00e9p\u00e8te <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> \u00e9preuves de Bernoulli identiques et ind\u00e9pendantes.<\/p>\n<p><img loading=\"lazy\" class=\"wp-image-81996 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/12\/binomiale.jpeg\" alt=\"loi-binomiale-arbre\" width=\"464\" height=\"239\" \/><\/p>\n<p>Lorsque l&rsquo;on tire un \u00e9chantillon de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> \u00e9l\u00e9ments dans une population tr\u00e8s grande, sans remise, on n&rsquo;a pas un sch\u00e9ma de Bernoulli, mais on pourra approcher l&rsquo;ensemble des <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> tirages par un sch\u00e9ma de Bernoulli.<\/p>\n<h2>C. Variable al\u00e9atoire binomiale en Terminale<\/h2>\n<h3><b>1. D\u00e9finition d&rsquo;une variable al\u00e9atoire binomiale en Terminale<\/b><\/h3>\n<p>On consid\u00e8re une \u00e9preuve de Bernoulli dont la probabilit\u00e9 du succ\u00e8s est <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/>. On r\u00e9p\u00e8te <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> fois de fa\u00e7on ind\u00e9pendante cette \u00e9preuve et on note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> la variable al\u00e9atoire repr\u00e9sentant le nombre de succ\u00e8s \u00e0 l&rsquo;issue de cette succession d&rsquo;\u00e9preuves.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> suit une<i>\u00a0loi binomiale de param\u00e8tres\u00a0<\/i><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/> et on note\u00a0<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7a47e00b482110aba3eb78c72e4f5a9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#92;&#104;&#111;&#111;&#107;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#123;&#66;&#125;&#40;&#110;&#32;&#44;&#32;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<h3><b>2. Formule de la loi binomiale<\/b><\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-90dfe4768bfa5842274340262040a00b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#92;&#105;&#110;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#78;&#125;&#94;&#42;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"51\" style=\"vertical-align: -1px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-98efc19cd8e63402f64b24df3119f63f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#92;&#105;&#110;&#92;&#59;&#32;&#32;&#093;&#48;&#32;&#44;&#32;&#49;&#091;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"67\" style=\"vertical-align: -5px;\"\/>, si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> suit une loi binomiale de param\u00e8tres <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/>,<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f113f352168d3b16a8f3e8b41e919e16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#115;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"7\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8eb560af39b01516642fcdf26725de61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;&#40;&#92;&#79;&#109;&#101;&#103;&#97;&#41;&#32;&#61;&#32;&#091;&#92;&#33;&#091;&#48;&#44;&#92;&#44;&#32;&#110;&#093;&#92;&#33;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"\/>,<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f113f352168d3b16a8f3e8b41e919e16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#115;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"7\" style=\"vertical-align: 0px;\"\/> pour tout <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-05ca2ec1c7b99253a8fb90e18d480b36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#48;&#44;&#92;&#44;&#32;&#110;&#093;&#92;&#33;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"74\" style=\"vertical-align: -5px;\"\/>, <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0524c19a130198bcc68451f6398e678d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#61;&#32;&#107;&#41;&#32;&#61;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#98;&#105;&#110;&#111;&#109;&#32;&#110;&#32;&#107;&#32;&#92;&#44;&#32;&#112;&#32;&#94;&#107;&#32;&#92;&#44;&#32;&#40;&#49;&#32;&#45;&#32;&#112;&#41;&#32;&#94;&#123;&#110;&#32;&#45;&#32;&#107;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"237\" style=\"vertical-align: -17px;\"\/>.<\/p>\n<h3><b>3. Esp\u00e9rance et variance de la loi binomiale<\/b><\/h3>\n<p>Si <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> suit une loi binomiale de param\u00e8tres <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/>,<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7c48445c57a405c883ba290e0a3415e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#114;&#109;&#123;&#69;&#125;&#40;&#88;&#41;&#32;&#61;&#32;&#110;&#32;&#92;&#44;&#32;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4e00aea1ab078755649e1f7f1525726d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#114;&#109;&#123;&#86;&#125;&#40;&#88;&#41;&#32;&#61;&#32;&#110;&#92;&#44;&#32;&#112;&#92;&#44;&#32;&#40;&#49;&#32;&#45;&#32;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"145\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p><img loading=\"lazy\" class=\"wp-image-81997 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/12\/loi-binomiale-parametres.png\" alt=\"loi-binomiale-parametres\" width=\"336\" height=\"236\" \/><\/p>\n<h3><b>4. Intervalle de fluctuation de la loi binomiale<\/b><\/h3>\n<p>Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> une variable al\u00e9atoire de loi <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ca47d4135bd669345fabc5f176714c4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#66;&#125;&#40;&#110;&#32;&#44;&#32;&#112;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-192c696d155f9af083adfeee791ef3f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#92;&#105;&#110;&#32;&#92;&#59;&#32;&#093;&#48;&#32;&#44;&#32;&#49;&#091;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"69\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Il existe deux entiers <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> tels que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d10554184def8855c17f5332a3875a4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#97;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#88;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#98;&#32;&#41;&#32;&#92;&#103;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#49;&#32;&#45;&#32;&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"170\" style=\"vertical-align: -5px;\"\/> .<\/p>\n<p>On dit que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-56a857be1f8515c67d722764b1f19efa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#091;&#92;&#33;&#091;&#97;&#32;&#44;&#92;&#44;&#32;&#98;&#093;&#92;&#33;&#093;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"38\" style=\"vertical-align: -5px;\"\/> est un\u00a0<i>intervalle de fluctuation<\/i>\u00a0pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/>\u00a0<i>au risque<\/i>\u00a0<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8f0b6b1a01f8fcc2f95be0364c090397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> ou\u00a0<i>au seuil\u00a0<\/i><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-36eb60cf13320e61a426ac47795a67b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#32;&#45;&#32;&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"\/><\/p>\n<p>En pratique, on cherche le plus grand entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> et le plus petit entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> tels que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d10554184def8855c17f5332a3875a4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#97;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#88;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#98;&#32;&#41;&#32;&#92;&#103;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#49;&#32;&#45;&#32;&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"170\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Si l&rsquo;on impose : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> est le plus grand entier tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-278cb86cac09bfe0ec5ec7274a2bae58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#32;&#40;&#32;&#88;&#32;&#60;&#32;&#97;&#32;&#41;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"111\" style=\"vertical-align: -12px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\"\/> le plus petit entier tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-08762492094dca679efff3203c276ca6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#32;&#40;&#32;&#88;&#32;&#62;&#32;&#98;&#32;&#41;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"110\" style=\"vertical-align: -12px;\"\/>,<br \/>\nalors <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d10554184def8855c17f5332a3875a4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#97;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#88;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#98;&#32;&#41;&#32;&#92;&#103;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#49;&#32;&#45;&#32;&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"170\" style=\"vertical-align: -5px;\"\/>.<\/p>\n<p>On dit que l<i>&lsquo;intervalle de fluctuation est centr\u00e9<\/i>.<\/p>\n<p><img loading=\"lazy\" class=\"wp-image-81998 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/12\/intervalle-centre.png\" alt=\"intervalle-fluctuation-centre\" width=\"413\" height=\"309\" \/><\/p>\n<p>&nbsp;<\/p>\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"188470\" class=\"elementor elementor-188470\">\n\t\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t<section class=\"has_ae_slider elementor-section elementor-inner-section elementor-element elementor-element-631306ea elementor-section-content-bottom full_width elementor-section-full_width elementor-section-height-min-height elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"631306ea\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-narrow\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-6563f946 ae-bg-gallery-type-default\" data-id=\"6563f946\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6683ddba elementor-widget elementor-widget-heading\" data-id=\"6683ddba\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">UN PROF DE MATHS POUR EXCELLER<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-368ff731 elementor-widget elementor-widget-heading\" data-id=\"368ff731\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">La pratique et la compr\u00e9hension <br\/> cl\u00e9s de la r\u00e9ussite<\/b><\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3481b8e7 elementor-widget elementor-widget-heading\" data-id=\"3481b8e7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Cours de maths en ligne ou \u00e0 domicile<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5b36e2da elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"5b36e2da\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\" target=\"_blank\" class=\"elementor-button-link elementor-button elementor-size-md\" role=\"button\" id=\"CTA_PRD_CP\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Professeur particulier de maths<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-44ee3437 elementor-widget elementor-widget-text-editor\" data-id=\"44ee3437\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p style=\"text-align: left;\"><b>Avis Google France <\/b><span style=\"color: #e5a430;\"><b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span><b> 4,9 sur 5<\/b><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_ae_slider elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-5189cb59 ae-bg-gallery-type-default\" data-id=\"5189cb59\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\n<p>&nbsp;<\/p>\n<h2>D. Utilisation de Python pour mod\u00e9liser la loi binomiale<\/h2>\n<h3><b>1. D\u00e9terminer la loi d&rsquo;une variable al\u00e9atoire binomiale<\/b><\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/>\u00a0<i>La loi\u00a0<\/i><br \/>\nfrom math import factorial as fact<\/p>\n<p>def binom(n, p, k):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return fact(n)\/fact(k)\/fact(n <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4d9521b52a5c0a70956f069f1dbcd50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"12\" style=\"vertical-align: 4px;\"\/>k)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-73be8cf29f235125f563fada8b04cfc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\"\/> * p **k * (1 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4d9521b52a5c0a70956f069f1dbcd50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"12\" style=\"vertical-align: 4px;\"\/>p) **(n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4d9521b52a5c0a70956f069f1dbcd50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"12\" style=\"vertical-align: 4px;\"\/> k)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/><i>\u00a0Calcul des probabilit\u00e9s cumul\u00e9es<\/i>\u00a0:<br \/>\npour obtenir <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-6b75e95a554a3af39b7fa001e8e33793_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#40;&#107;&#41;&#32;&#61;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#32;&#92;&#115;&#117;&#109;&#32;&#95;&#32;&#123;&#105;&#32;&#61;&#32;&#48;&#125;&#32;&#94;&#107;&#32;&#92;&#44;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#61;&#32;&#105;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"162\" style=\"vertical-align: -21px;\"\/><\/p>\n<p>def cumulbinom(n, p, k):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S = 0<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for i in range(k + 1):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0c504f54a3388252aea42179bc59f413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S = S +\u00a0 binom(n, p, i)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return S<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Pour obtenir la liste des <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9d0819a1b3f6ed9e8eab2908ac93fcf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#40;&#107;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"37\" style=\"vertical-align: -5px;\"\/> pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4625859e51b6f1a79e03da7e4ab3fa7a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#107;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"77\" style=\"vertical-align: -3px;\"\/> :<br \/>\ndef TablCumul(n, p):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> T=[]\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S = 0<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for k in range (n + 1):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S= S +binom(n, p, k)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> T.append(S)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return T<\/p>\n<p>Toutes ces <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fonctions-trigonometriques-terminale\/\">fonctions<\/a> ne sont utilisables que pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-069827556d9004b7fbc50b3fc61e6716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#49;&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -3px;\"\/>.<\/p>\n<h3><b>2. Graphique de loi binomiale avec Python<\/b><\/h3>\n<p>Dans les deux cas :<br \/>\nimport matplotlib.pyplot as plt<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Diagramme en b\u00e2tons de la loi d&rsquo;une variable de Bernoulli (en rouge)<br \/>\ndef batons(n,p):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for k in range(0 , n + 1):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> plt.plot([k, k],<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-86e37f6c94f18e5c8e45b102a3bbb9bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\"\/> [0 , binom(n , p, k) ], &lsquo;r&rsquo;)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> plt.show()<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> En utilisant \u00ab\u00a0bar\u00a0\u00bb<br \/>\nremplacer <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/> par leurs valeurs :<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f113f352168d3b16a8f3e8b41e919e16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#115;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"7\" style=\"vertical-align: 0px;\"\/> D\u00e9terminer dans une liste la loi de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/><br \/>\nloi = [binom(n,p,k) for k in range(n + 1)]\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f113f352168d3b16a8f3e8b41e919e16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#115;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"7\" style=\"vertical-align: 0px;\"\/> et utilisation de bar ;<br \/>\nplt.bar(range(n +1 ), loi, width = 0.1)<\/p>\n<p><b>3. Simuler un tirage de Bernoulli, binomial, avec Python<\/b><\/p>\n<p>Dans tous les cas,<br \/>\nimport random<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/>\u00a0<i>Simulation d&rsquo;une loi de Bernoulli<\/i>\u00a0:<br \/>\ndef SimulBernoulli(p):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> a = random.random()<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> if a &lt; p:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> else:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return 0<\/p>\n<p>et pour obtenir 20 simulations d&rsquo;une loi de Bernoulli de param\u00e8tre <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1e4419032e9b2a7c997243dc95aced4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\"\/><br \/>\n[SimulBernoulli(0.8) for k in range (20)]\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/>\u00a0<i>Simulation d&rsquo;une loi binomiale<\/i><br \/>\ndef SimulBinomiale(n,p):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> res = 0<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for k in range (n):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> if SimulBernoulli(p) == 1:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-92bc932f1773cd516b4a112f273df627_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> res = res + 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return(res)<\/p>\n<p>et pour obtenir 20 simulations d&rsquo;une loi binomiale de param\u00e8tres 10 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b7ab7f7da74090c2370accce55f96e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\"\/><br \/>\n[SimulBinomiale(10,0.5) for k in range (20)]\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/>\u00a0<i>R\u00e9p\u00e9tition de\u00a0<\/i><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-58c9e0499df9a4ae51c8689c9b256212_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#78;&#98;&#101;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\"\/>\u00a0<i>simulations d&rsquo;une loi binomiale\u00a0<\/i><br \/>\ndef RepeteSimulBinomiale(n, p, Nbe):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> L = [0]*(n + 1)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for k in range(Nfois):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> res = SimulBinomiale(n, p)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> L[res] = L[res] + 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return(L)<\/p>\n<p>et pour obtenir 20 simulations d&rsquo;une loi binomiale de param\u00e8tres 10 et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0ca16220aa3a1a1ea2d54c4f940a0f59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\"\/>, suivies de la repr\u00e9sentation :<br \/>\nLL= RepeteSimulBinomiale(10, 0.4, 20)<br \/>\nplt.bar(range(11 ), LL, width = 0.1)<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/>\u00a0<i>Calcul des fr\u00e9quences des occurrences lors de\u00a0<\/i><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-58c9e0499df9a4ae51c8689c9b256212_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#78;&#98;&#101;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\"\/>\u00a0<i>simulations d&rsquo;une loi binomiale de param\u00e8tres<\/i>\u00a0<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b170995d512c659d8668b4e42e1fef6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"\/><br \/>\ndef FrequenceSimulBinomiale(n,p, Nbe):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> L = [0]*(n + 1)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for k in range(Nbe):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> res = SimulBinomiale(n, p)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> L[res] = L[res] + 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> for k in range(n + 1):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> L[k] = L[k] \/Nbe<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return(L)<\/p>\n<p>et exemple de repr\u00e9sentation (10000 simulations) :<br \/>\nF = FrequenceSimulBinomiale(10,0.4,10000)<br \/>\nplt.bar(range(11 ), F, width = 0.1)<\/p>\n<p><img loading=\"lazy\" class=\"wp-image-82110 aligncenter\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/12\/python-loi-binomiale.png\" alt=\"loi-binomiale-python\" width=\"424\" height=\"316\" \/><\/p>\n<h3><b>4. Probl\u00e8mes de seuils avec une variable <\/b>X<b>\u00a0de loi binomiale<\/b><\/h3>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Proc\u00e9dure qui donne le plus grand entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-250cc896da7f026bb00720740c7a8390_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#32;&#40;&#88;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#107;&#32;&#41;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"\/> :<\/p>\n<p>def SeuilGauche(n, p, alpha):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S = binom(n, p, 0)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> k = 0<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> while S &lt;= alpha:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0c504f54a3388252aea42179bc59f413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> k = k + 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0c504f54a3388252aea42179bc59f413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S = S + binom(n, p, k)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return k <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4d9521b52a5c0a70956f069f1dbcd50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"12\" style=\"vertical-align: 4px;\"\/>1<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Proc\u00e9dure qui donne le plus petit entier <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\"\/> tel que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f9e7fc5a27dce4703e0c7543a0a2712a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#80;&#125;&#40;&#88;&#32;&#92;&#103;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#107;&#32;&#41;&#32;&#92;&#108;&#101;&#113;&#115;&#108;&#97;&#110;&#116;&#32;&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"109\" style=\"vertical-align: -5px;\"\/> :<\/p>\n<p>def SeuilDroit(n, p, alpha):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S =\u00a0 binom(n, p, n)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> k = n<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> while S &lt;= alpha:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> k = k &#8211; 1<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-10486d8a61d2829e287406ae7d12f3c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> S = S + binom(n, p, k)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return k + 1<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2b6e225d778ccd32cb2bd9cc4eaead9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#117;&#108;&#108;&#101;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"7\" width=\"8\" style=\"vertical-align: 1px;\"\/> Proc\u00e9dure qui donne l&rsquo;intervalle de fluctuation centr\u00e9 de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d4ee28752517d6062a3ca0314890342d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\"\/> au seuil de risque <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8f0b6b1a01f8fcc2f95be0364c090397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/> :<\/p>\n<p>def IntervalleFluc(n, p, risque):<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> m = SeuilGauche(n, p, risque\/2)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> M = SeuilDroit(n, p, risque\/2)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0aff0c2670620b7a12cf322b091e3be1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#113;&#117;&#97;&#100;&#92;&#118;&#101;&#114;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"1\" style=\"vertical-align: -5px;\"\/> return [m+1, M<img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4d9521b52a5c0a70956f069f1dbcd50e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"12\" style=\"vertical-align: 4px;\"\/>1]\n<div class=\"style_pag\" style=\"color: #000;font-family: 'Lato', Sans-serif\">\n<p>Voici quelques autres chapitres de Math\u00e9matiques de Terminale, \u00e0 conna\u00eetre aussi pour r\u00e9ussir son Bac :<\/p>\n<ul>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-loi-grands-nombres-terminale\/\">loi des grands nombres\u00a0<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-normale-fluctuation-estimation\/\">loi Normale, intervalle de fluctuation<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-recurrence-terminale\/\">raisonnement par r\u00e9currence<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-suites-terminale\/\">les suites<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-limites-fonctions-terminale\/\">les limites<\/a><\/li>\n<\/ul>\n<p style=\"text-align: justify\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>La loi binomiale en Terminale G\u00e9n\u00e9rale R\u00e9sum\u00e9 de cours Exercices et corrig\u00e9s Cours en ligne de Maths en Terminale A. \u00c9preuves ind\u00e9pendantes en Terminale 1. D\u00e9finition des \u00e9preuves ind\u00e9pendantes en Terminale Soit , . Soient \u00e9preuves pour . On note l&rsquo;univers (suppos\u00e9 fini) des r\u00e9sultats \u00e9l\u00e9mentaires associ\u00e9s \u00e0 l&rsquo;\u00e9preuve \u00a0 et la probabilit\u00e9 asso- ci\u00e9e. [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.2.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Loi binomiale en Terminale G\u00e9n\u00e9rale : cours complet<\/title>\n<meta name=\"description\" content=\"Retrouvez notre cours complet sur la Loi Binomiale en Terminale : formule, application, esp\u00e9rance variance etc. , pour \u00eatre au point au bac.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Loi binomiale en Terminale G\u00e9n\u00e9rale : cours complet\" \/>\n<meta property=\"og:description\" content=\"Retrouvez notre cours complet sur la Loi Binomiale en Terminale : formule, application, esp\u00e9rance variance etc. , pour \u00eatre au point au bac.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\" \/>\n<meta property=\"og:site_name\" content=\"Groupe R\u00e9ussite\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/GroupeReussiteOfficiel\/\" \/>\n<meta property=\"article:modified_time\" content=\"2023-09-15T12:21:45+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/12\/binomiale.jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:site\" content=\"@GroupeReussite\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\",\"name\":\"Loi binomiale en Terminale G\u00e9n\u00e9rale : cours complet\",\"isPartOf\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\"},\"datePublished\":\"2020-12-17T10:17:55+00:00\",\"dateModified\":\"2023-09-15T12:21:45+00:00\",\"description\":\"Retrouvez notre cours complet sur la Loi Binomiale en Terminale : formule, application, esp\u00e9rance variance etc. , pour \u00eatre au point au bac.\",\"breadcrumb\":{\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/#breadcrumb\"},\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-loi-binomiale-terminale\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Accueil\",\"item\":\"https:\/\/groupe-reussite.fr\/ressources\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cours sur la loi binomiale en Terminale\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/groupe-reussite.fr\/ressources\/#website\",\"url\":\"https:\/\/groupe-reussite.fr\/ressources\/\",\"name\":\"Groupe R\u00e9ussite - 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