{"id":34220,"date":"2019-08-19T10:11:58","date_gmt":"2019-08-19T09:11:58","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=34220"},"modified":"2022-07-20T11:21:32","modified_gmt":"2022-07-20T10:21:32","slug":"cours-en-ligne-exercices-probabilites-univers-fini-ecs1","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-probabilites-univers-fini-ecs1\/","title":{"rendered":"Probabilit\u00e9s sur un univers fini en ECG1 &#8211; Exercices"},"content":{"rendered":"<div class=\"Latex_page\">\r\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\">\r\n<div class=\"elementor-container elementor-column-gap-no\">\r\n<div class=\"elementor-row\">\r\n<div class=\"elementor-column-wrap elementor-element-populated colone_elementor\">\r\n\t\t<div data-elementor-type=\"page\" data-elementor-id=\"88449\" class=\"elementor elementor-88449\">\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-30229867 elementor-section-content-bottom elementor-hidden-mobile elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"30229867\" 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-6a356d88 sticky_badeau_colone strick_col elementor-hidden-mobile ae-bg-gallery-type-default\" data-id=\"6a356d88\" 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-7ccae7e7 elementor-hidden-mobile elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"7ccae7e7\" 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-6e77d559 strick_col ae-bg-gallery-type-default\" data-id=\"6e77d559\" 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-17b9742a elementor-widget elementor-widget-heading\" data-id=\"17b9742a\" 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-ecs1\/\">Cours en ligne Maths en ECG1<\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73a4684f elementor-widget elementor-widget-heading\" data-id=\"73a4684f\" 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 ECG1<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ebcc4f9 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ebcc4f9\" 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-exercices-strategies-calcul-ecs1\/\" 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\">Strat\u00e9gie de Calcul<\/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-7ff87283 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"7ff87283\" 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-espace-probabilise-ecs1\/\" 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\">Espace Probabilis\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-57d652c3 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"57d652c3\" 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-raisonnement-ensembliste-ecs1\/\" 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 Vocabulaire Ensembliste<\/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-65809d15 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"65809d15\" 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-ecs1\/\" 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<\/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-55f287a9 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"55f287a9\" 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-ecs1\/\" 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\">Polyn\u00f4mes<\/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-5de71e57 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5de71e57\" 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-reelles-ecs1\/\" 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\">Suites R\u00e9elles<\/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-2e13b47d elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2e13b47d\" 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-ecs1\/\" 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-b80cd71 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b80cd71\" 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-espaces-vectoriels-ecs1\/\" 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\">Espaces Vectoriels et Applications Lin\u00e9aires<\/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-515ac59b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"515ac59b\" 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-variables-reelles-ecs1\/\" 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 R\u00e9elles \u00e0 Variables R\u00e9elles<\/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-37b7a48c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"37b7a48c\" 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-probabilites-univers-fini-ecs1\/\" 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\">Probabilit\u00e9s (univers infini)<\/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-a165fbf elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"a165fbf\" 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-formules-taylor-developpements-limites-ecs1\/\" 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\">Formules de Taylor et D\u00e9veloppements Limit\u00e9s<\/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-444d2f06 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"444d2f06\" 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-extrema-convexite-ecs1\/\" 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\">Extrema 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-f57142c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f57142c\" 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-series-numeriques-ecs1\/\" 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\">S\u00e9ries Num\u00e9riques<\/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-51fc1a2 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"51fc1a2\" 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-ecs1\/\" 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\">Int\u00e9gration<\/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-b8561ca elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b8561ca\" 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-finies-ecs1\/\" 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\">Variables Al\u00e9atoires Finies<\/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-c2a9e2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"c2a9e2f\" 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-discretes-ecs1\/\" 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\">Variables Al\u00e9atoires Discr\u00e8tes<\/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-6a7fab3 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6a7fab3\" 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-densite-ecs1\/\" 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\">Variables Al\u00e9atoires \u00e0 Densit\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-8b2a052 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8b2a052\" 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-convergences-approximations-ecs1\/\" 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\">Convergence et Approximations<\/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-3275bf4d elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3275bf4d\" 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<section class=\"has_ae_slider elementor-section elementor-top-section elementor-element elementor-element-7b89084 elementor-hidden-desktop elementor-hidden-tablet elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"7b89084\" 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-78ae9e4 ae-bg-gallery-type-default\" data-id=\"78ae9e4\" 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-2e97065 elementor-widget elementor-widget-heading\" data-id=\"2e97065\" 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-ecs1\/\">Cours en ligne Maths en ECG1<\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-eafadd7 elementor-widget elementor-widget-heading\" data-id=\"eafadd7\" 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 ECG1<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8180968 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8180968\" 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-exercices-strategies-calcul-ecs1\/\" 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\">Strat\u00e9gie de Calcul<\/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-38acf6a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"38acf6a\" 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-espace-probabilise-ecs1\/\" 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\">Espace Probabilis\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-b7ca681 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b7ca681\" 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-raisonnement-ensembliste-ecs1\/\" 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 Vocabulaire Ensembliste<\/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-33a3c17 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"33a3c17\" 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-ecs1\/\" 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<\/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-ccd9c89 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ccd9c89\" 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-ecs1\/\" 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\">Polyn\u00f4mes<\/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-51de2d5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"51de2d5\" 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-reelles-ecs1\/\" 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\">Suites R\u00e9elles<\/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-ef0680e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"ef0680e\" 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-ecs1\/\" 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-5bb4a9c elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"5bb4a9c\" 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-espaces-vectoriels-ecs1\/\" 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\">Espaces Vectoriels et Applications Lin\u00e9aires<\/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-f4868e8 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"f4868e8\" 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-variables-reelles-ecs1\/\" 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 R\u00e9elles \u00e0 Variables R\u00e9elles<\/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-87d53c5 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"87d53c5\" 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-probabilites-univers-fini-ecs1\/\" 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\">Probabilit\u00e9s (univers infini)<\/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-87744be elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"87744be\" 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-formules-taylor-developpements-limites-ecs1\/\" 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\">Formules de Taylor et D\u00e9veloppements Limit\u00e9s<\/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-41f4808 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"41f4808\" 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-extrema-convexite-ecs1\/\" 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\">Extrema 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-77acc16 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"77acc16\" 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-series-numeriques-ecs1\/\" 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\">S\u00e9ries Num\u00e9riques<\/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-672728a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"672728a\" 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-ecs1\/\" 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\">Int\u00e9gration<\/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-52a2f88 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"52a2f88\" 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-finies-ecs1\/\" 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\">Variables Al\u00e9atoires Finies<\/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-6c1102b elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6c1102b\" 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-discretes-ecs1\/\" 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\">Variables Al\u00e9atoires Discr\u00e8tes<\/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-cd78ac0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"cd78ac0\" 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-densite-ecs1\/\" 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\">Variables Al\u00e9atoires \u00e0 Densit\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-52d8afc elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"52d8afc\" 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-convergences-approximations-ecs1\/\" 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\">Convergence et Approximations<\/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-b364a45 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"b364a45\" 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\r\n<\/div>\r\n<div class=\"elementor-column-wrap elementor-element-populated colone_latex\">\r\n<div class=\"style_pag\" style=\"color: #000; font-family: 'Lato', Sans-serif;\">\r\n<div class=\"elementor-text-editor elementor-clearfix\">\r\n<h1 class=\"Latex_page_title\">Exercices : Probabilit\u00e9s sur un univers fini en ECG1<\/h1>\r\n<\/div>\r\n<p class=\"colone_latex_ancres\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites-univers-fini-ecs1\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-probabilites-univers-fini-ecs1\/\">Exercices<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-corriges-probabilites-univers-fini-ecs1\/\">Corrig\u00e9s<\/a><\/p>\r\n<p class=\"colone_latex_ancres\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-ecs1\/\">Cours en ligne de Maths en ECG1<\/a><\/p>\r\n<p><\/p>\r\n<h2 style=\"text-align: justify;\">Exercices &#8211; Probabilit\u00e9s sur un univers fini<\/h2>\r\n<h3 style=\"text-align: justify;\"><b>Exercice 1 :\u00a0<\/b><\/h3>\r\n<p style=\"text-align: justify;\">Une urne contient <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;\"\/> boules distinctes num\u00e9rot\u00e9es de <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\"\/> \u00e0 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7ecab3f5df4767e23a2660ceb88ceabd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> On effectue un tirage de <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;\"\/> boules avec <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0426d9150d2f337715d22a39d16f7f8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#32;&#49;&#44;&#32;&#110;&#32;&#093;&#92;&#33;&#093;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p style=\"text-align: justify;\"><b>1)<\/b>\u00a0On suppose dans cette question que les <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;\"\/> boules sont extraites simultan\u00e9ment. Combien y a-t-il de tirages possibles ?<\/p>\r\n<p style=\"text-align: justify;\"><b>2)<\/b>\u00a0Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-59433101b976c2e2e0bb06137873843c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#32;&#112;&#32;&#44;&#32;&#110;&#32;&#093;&#92;&#33;&#093;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"77\" style=\"vertical-align: -5px;\"\/> D\u00e9terminer le nombre de tirages tels que :<\/p>\r\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0a)<\/b>\u00a0toutes les boules obtenues ont un num\u00e9ro inf\u00e9rieur ou \u00e9gal \u00e0 k,<\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>b)<\/b>\u00a0le plus grand num\u00e9ro est <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-4a22b46fd6f4018a6b70bc870f75be7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0\u00a0<b>\u00a0c)<\/b>\u00a0En d\u00e9duire que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-705f77732a27c74cf18918a9681f8197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#115;&#117;&#109;&#95;&#123;&#107;&#61;&#112;&#125;&#94;&#110;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#107;&#32;&#45;&#32;&#49;&#125;&#123;&#112;&#32;&#45;&#32;&#49;&#125;&#32;&#61;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#125;&#123;&#112;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"53\" width=\"159\" style=\"vertical-align: -25px;\"\/><\/p>\r\n<p style=\"text-align: justify;\"><b>3)\u00a0<\/b>On suppose dans cette question que les tirages sont successifs et sans remise.<\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>a)<\/b>\u00a0Combien y a-t-il de tirages possibles ?<\/p>\r\n<p style=\"text-align: justify;\"><b>\u00a0 \u00a0 \u00a0b)<\/b>\u00a0Combien y a-t-il de tirages commen\u00e7ant par la boule num\u00e9ro <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/> ?<\/p>\r\n<p style=\"text-align: justify;\"><b>4)<\/b>\u00a0On suppose dans cette question que les tirages sont successifs et avec remise.<\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>a)<\/b>\u00a0Combien y a-t-il de tirages possibles ?<\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>b)<\/b>\u00a0Combien y a-t-il de tirages pour lesquels le premier num\u00e9ro obtenu est strictement inf\u00e9rieur au dernier ?<\/p>\r\n<p>&nbsp;<\/p>\r\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"84983\" class=\"elementor elementor-84983\">\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-51d9c4d 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=\"51d9c4d\" 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-610eeeb9 ae-bg-gallery-type-default\" data-id=\"610eeeb9\" 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-5bf69eb8 elementor-widget elementor-widget-heading\" data-id=\"5bf69eb8\" 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<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-49568da4 elementor-widget elementor-widget-heading\" data-id=\"49568da4\" 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 professeurs particuliers<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1eb9e0cb elementor-widget elementor-widget-heading\" data-id=\"1eb9e0cb\" 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\">Pour progresser et r\u00e9ussir<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-15c3e28d elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"15c3e28d\" 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\">Cours particuliers 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-1a5c10e7 elementor-widget elementor-widget-text-editor\" data-id=\"1a5c10e7\" 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-6913d4fe ae-bg-gallery-type-default\" data-id=\"6913d4fe\" 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\r\n<p>&nbsp;<\/p>\r\n<h3 style=\"text-align: justify;\"><b>Exercice 2 :\u00a0<\/b><\/h3>\r\n<p style=\"text-align: justify;\">Soient <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 <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;\"\/> deux entiers naturels non nuls. On note <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-28bf3d71039b1d98ef4e8662f7de2c05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#95;&#110;&#94;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"19\" style=\"vertical-align: -2px;\"\/> le nombre de surjections d&rsquo;un ensemble \u00e0 <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;\"\/> \u00e9l\u00e9ments dans un ensemble \u00e0 <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.<\/p>\r\n<p style=\"text-align: justify;\"><b>1) a)<\/b>\u00a0Pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0072b5dbe18174a024a7c7388c8149d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#32;&#62;&#32;&#112;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"47\" style=\"vertical-align: -4px;\"\/> calculer <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-0b7899cec886711499395b80cbc7a4e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#95;&#110;&#94;&#112;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"24\" style=\"vertical-align: -2px;\"\/><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>b)<\/b>\u00a0Pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-83ef6d7af410025404eed3295d06357b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#92;&#105;&#110;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#98;&#123;&#78;&#125;&#94;&#42;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -4px;\"\/> calculer <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-9a4d6f6a725bd5247835ed84b65a48c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#95;&#112;&#94;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"19\" style=\"vertical-align: -5px;\"\/> et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-35910849c05d322babf6ca88d805bf28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#95;&#49;&#94;&#112;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"24\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>c)<\/b>\u00a0Montrer que pour tout <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e9a90e8b52b4c3d7fbc01072f8d0365c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#32;&#92;&#103;&#101;&#32;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-13c2b39de4ae06ed213fd5327e35de3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#95;&#50;&#94;&#112;&#32;&#61;&#32;&#50;&#94;&#112;&#32;&#45;&#32;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"95\" style=\"vertical-align: -5px;\"\/><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>d)<\/b>\u00a0Montrer que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3d18716a7b8327a727791c093a7accb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#95;&#110;&#94;&#123;&#110;&#32;&#43;&#32;&#49;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#50;&#125;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#32;&#43;&#32;&#49;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#33;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"141\" style=\"vertical-align: -6px;\"\/><\/p>\r\n<p style=\"text-align: justify;\"><b>2)<\/b>\u00a0Soient <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 <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;\"\/> deux entiers naturels tels que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1e769fbc7a8d8dd1f00361caa1ab6e57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#32;&#92;&#108;&#101;&#32;&#110;&#32;&#92;&#108;&#101;&#32;&#112;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -4px;\"\/><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>a)\u00a0<\/b>Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-96d2278114a6add6666fb401907adb2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#32;&#49;&#32;&#44;&#32;&#110;&#32;&#45;&#32;&#49;&#32;&#093;&#92;&#33;&#093;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"106\" style=\"vertical-align: -5px;\"\/> \u00e9tablir que : pour <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2f0f1caa4a5251770d725224cf6d54b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#32;&#113;&#32;&#44;&#32;&#110;&#32;&#093;&#92;&#33;&#093;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"76\" style=\"vertical-align: -5px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1f0eefb3e55113f4eaffb165d988f30b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#125;&#123;&#107;&#125;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#107;&#125;&#123;&#113;&#125;&#32;&#61;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#125;&#123;&#113;&#125;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#32;&#45;&#32;&#113;&#125;&#123;&#107;&#32;&#45;&#32;&#113;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"201\" style=\"vertical-align: -17px;\"\/>\u00a0<\/p>\r\n<p style=\"text-align: justify;\">En d\u00e9duire :<\/p>\r\n<p style=\"text-align: justify;\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 53px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-656ef6a2fa59a08799fa2fa3ea3b6757_l3.png\" height=\"53\" width=\"185\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#115;&#117;&#109;&#95;&#123;&#107;&#61;&#113;&#125;&#94;&#110;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#45;&#32;&#49;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#107;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#125;&#123;&#107;&#125;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#107;&#125;&#123;&#113;&#125;&#32;&#61;&#32;&#48;&#46;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0 \u00a0<b>b)<\/b>\u00a0Soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8b5614282fc97dbe3369d6e9acdf7ee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#105;&#32;&#92;&#105;&#110;&#32;&#091;&#92;&#33;&#091;&#32;&#49;&#32;&#44;&#32;&#110;&#32;&#093;&#92;&#33;&#093;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"73\" style=\"vertical-align: -5px;\"\/> On pose <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-a6bfc37b2ba02c017dee96d4298e128b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#32;&#65;&#95;&#105;&#32;&#61;&#32;&#92;&#108;&#101;&#102;&#116;&#92;&#123;&#32;&#102;&#32;&#92;&#105;&#110;&#32;&#70;&#94;&#69;&#44;&#32;&#92;&#44;&#32;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#99;&#97;&#114;&#100;&#125;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#102;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#69;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#32;&#61;&#32;&#105;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#92;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"261\" style=\"vertical-align: -7px;\"\/> Justifier que <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-7bbb3102729acd248d5ae432276ad2fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#70;&#94;&#69;&#32;&#61;&#32;&#92;&#98;&#105;&#103;&#99;&#117;&#112;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#110;&#32;&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#32;&#65;&#95;&#105;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"114\" style=\"vertical-align: -6px;\"\/> En d\u00e9duire que :<\/p>\r\n<p style=\"text-align: justify;\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 49px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-bdd0052033997bd6d1a94908c476b638_l3.png\" height=\"49\" width=\"131\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#110;&#94;&#112;&#32;&#61;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#115;&#117;&#109;&#95;&#123;&#105;&#61;&#49;&#125;&#94;&#110;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#125;&#123;&#105;&#125;&#32;&#83;&#95;&#105;&#94;&#112;&#46;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\r\n<p style=\"text-align: justify;\">\u00a0 \u00a0\u00a0<b>\u00a0c)<\/b>\u00a0En d\u00e9duire :<\/p>\r\n<p style=\"text-align: justify;\"><p class=\"ql-center-displayed-equation\" style=\"line-height: 50px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b275da3f958372623bd4a93c733b2dda_l3.png\" height=\"50\" width=\"227\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#091;&#83;&#95;&#110;&#94;&#112;&#32;&#61;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#45;&#32;&#49;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#110;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#115;&#117;&#109;&#95;&#123;&#107;&#61;&#48;&#125;&#94;&#110;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#32;&#45;&#32;&#49;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#94;&#107;&#32;&#92;&#100;&#105;&#115;&#112;&#108;&#97;&#121;&#115;&#116;&#121;&#108;&#101;&#92;&#98;&#105;&#110;&#111;&#109;&#123;&#110;&#125;&#123;&#107;&#125;&#32;&#107;&#94;&#112;&#46;&#92;&#093;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\u00a0<\/p>\r\n<p>&nbsp;<\/p>\r\n\t\t<div data-elementor-type=\"section\" data-elementor-id=\"127774\" class=\"elementor elementor-127774\">\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-5a7b6a2a 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=\"5a7b6a2a\" 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-749af387 ae-bg-gallery-type-default\" data-id=\"749af387\" 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-1b4ed465 elementor-widget elementor-widget-heading\" data-id=\"1b4ed465\" 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 PARTICULIERS EN LIGNE<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-16d47760 elementor-widget elementor-widget-heading\" data-id=\"16d47760\" 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\">Nous avons s\u00e9lectionn\u00e9 pour vous les meilleurs professeurs particuliers.<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21a162bf elementor-widget elementor-widget-heading\" data-id=\"21a162bf\" 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\">POUR ACC\u00c9L\u00c9RER MA PROGRESSION<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5600477e elementor-align-left elementor-mobile-align-center elementor-widget elementor-widget-button\" data-id=\"5600477e\" 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-en-ligne\/toutes-matieres\/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\">Cours particuliers en ligne<\/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-1c7a7876 elementor-widget elementor-widget-text-editor\" data-id=\"1c7a7876\" 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-2aa12288 ae-bg-gallery-type-default\" data-id=\"2aa12288\" 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\r\n<p>&nbsp;<\/p>\r\n<p>De nombreux autres exercices et corrig\u00e9s d&rsquo;exercices sont disponibles sur tous les chapitres de maths en ECG1 :<\/p>\r\n<ul style=\"text-align: justify;\">\r\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-formules-taylor-developpements-limites-ecs1\/\">les formules de Taylor et les d\u00e9veloppements limit\u00e9s<\/a><\/li>\r\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-extrema-convexite-ecs1\/\">extrema et la convexit\u00e9<\/a><\/li>\r\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-series-numeriques-ecs1\/\">les s\u00e9ries num\u00e9riques<\/a><\/li>\r\n<li style=\"text-align: justify;\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-integration-ecs1\/\">l&rsquo;int\u00e9gration<\/a><\/li>\r\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-variables-aleatoires-finies-ecs1\/\">les variables al\u00e9atoires finies<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/section>\r\n<\/div>\r\n\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Exercices : Probabilit\u00e9s sur un univers fini en ECG1 R\u00e9sum\u00e9 de cours Exercices Corrig\u00e9s Cours en ligne de Maths en ECG1 Exercices &#8211; Probabilit\u00e9s sur un univers fini Exercice 1 :\u00a0 Une urne contient boules distinctes num\u00e9rot\u00e9es de \u00e0 On effectue un tirage de boules avec 1)\u00a0On suppose dans cette question que les boules sont [&hellip;]<\/p>\n","protected":false},"author":7,"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>Exercices sur les probabilit\u00e9s sur un univers fini en ECG1<\/title>\n<meta name=\"description\" content=\"Exercices 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