{"id":55661,"date":"2020-06-22T08:27:56","date_gmt":"2020-06-22T07:27:56","guid":{"rendered":"https:\/\/groupe-reussite.fr\/?page_id=55661"},"modified":"2024-10-17T06:35:17","modified_gmt":"2024-10-17T05:35:17","slug":"cours-en-ligne-probabilites","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/","title":{"rendered":"Cours en ligne de probabilit\u00e9"},"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<p style=\"text-align: justify\">\t\t<div data-elementor-type=\"page\" data-elementor-id=\"86176\" class=\"elementor elementor-86176\">\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-6f9fb2b3 elementor-section-content-bottom elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"6f9fb2b3\" 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-5032621c sticky_badeau_colone strick_col ae-bg-gallery-type-default\" data-id=\"5032621c\" 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-611bd75f elementor-section-boxed elementor-section-height-default elementor-section-height-default ae-bg-gallery-type-default\" data-id=\"611bd75f\" 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-55718945 strick_col ae-bg-gallery-type-default\" data-id=\"55718945\" 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-5940f45c elementor-widget elementor-widget-heading\" data-id=\"5940f45c\" 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-tage-mage\/\">Cours en ligne Tage Mage <\/a><\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f9bc725 elementor-widget elementor-widget-heading\" data-id=\"f9bc725\" 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 du sous-test 2 du Tage Mage<\/p>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-56c02cf0 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"56c02cf0\" 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-fractions\/\" 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\">Fractions<\/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-390da5ff elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"390da5ff\" 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-pourcentages\/\" 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\">Pourcentages<\/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-da8d658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"da8d658\" 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-corriges-algebre\/\" 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\">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-490ac2aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"490ac2aa\" 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-figures-geometriques\/\" 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<\/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-3fd40310 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"3fd40310\" 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-vitesse\/\" 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\">Vitesse<\/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-6edf1c7e elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6edf1c7e\" 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\/\" 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<\/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-4f2c805 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"4f2c805\" 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-puissances\/\" 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\">Puissances<\/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-447b658 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"447b658\" 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-regle-de-trois\/\" 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\">Proportionnalit\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-53863aa elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"53863aa\" 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\/\" 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-11741389 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"11741389\" 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\/\" 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<\/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-6ace8ace elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"6ace8ace\" 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-moyenne-arithmetique-moyenne-ponderee\/\" 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\">Moyenne<\/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-13f1db2f elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"13f1db2f\" 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-theoreme-de-pythagore\/\" 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\">Th\u00e9or\u00e8me de Pythagore<\/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-10d04684 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"10d04684\" 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-theoreme-de-thales\/\" 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\">Th\u00e9or\u00e8me de Thal\u00e8s<\/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-691a3a8a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"691a3a8a\" 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-racines-carrees\/\" 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\">Racines Carr\u00e9es<\/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-2a5f7bd6 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"2a5f7bd6\" 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\" style=\"color: #000000;font-family: Lato, sans-serif;text-align: justify\">\n<h1 class=\"Latex_page_title\">Probabilit\u00e9 : cours et formules de probabilit\u00e9 de base<\/h1>\n<\/div>\n<p class=\"colone_latex_ancres\" style=\"color: #000000;font-family: Lato, sans-serif;text-align: center\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-probabilites\/\">R\u00e9sum\u00e9 de cours<\/a> <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-probabilites\/\">Exercices et corrig\u00e9s<\/a><\/p>\n<p class=\"colone_latex_ancres\" style=\"color: #000000;font-family: Lato, sans-serif;text-align: center\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-tage-mage\/\">Cours en ligne du Tage Mage<\/a><\/p>\n<p style=\"text-align: justify\">Les probabilit\u00e9s accompagnent les \u00e9l\u00e8ves tout au long de leur scolarit\u00e9, du coll\u00e8ge \u00e0 la pr\u00e9paration du bac pour certains, mais aussi jusqu&rsquo;en pr\u00e9pa et pas uniquement en MPSI ou PCSI et pr\u00e9pa HEC. De plus, l&rsquo;\u00e9tude des probabilit\u00e9s commence tr\u00e8s t\u00f4t, en primaire, pour les plus pr\u00e9coces. Il est donc capital de comprendre les bases de ce domaine de cours de math\u00e9matiques, ce qui pourra vous servir m\u00eame en dehors des cours dans la vie quotidienne. Pour une meilleure compr\u00e9hension et ma\u00eetrise des probabilit\u00e9s au Tage Mage, nous vous recommandons de prendre des <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">cours de maths \u00e0 domicile<\/a>. Ces cours sont dispens\u00e9s par des profs de maths experts qui vous apporteront toutes les m\u00e9thodes de travail efficaces pour r\u00e9ussir au concours.<\/p>\n<h2 style=\"text-align: justify\">Formule probabilit\u00e9 de base :<\/h2>\n<p>proba = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-92d057501c705ecd91e6429605758cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#110;&#111;&#109;&#98;&#114;&#101;&#126;&#100;&#101;&#126;&#99;&#97;&#115;&#126;&#102;&#97;&#118;&#111;&#114;&#97;&#98;&#108;&#101;&#115;&#125;&#123;&#110;&#111;&#109;&#98;&#114;&#101;&#126;&#100;&#101;&#126;&#99;&#97;&#115;&#126;&#116;&#111;&#116;&#97;&#108;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"206\" style=\"vertical-align: -12px;\"\/><\/p>\n<p>Exemple type pour illustrer :<\/p>\n<p><span style=\"font-weight: 400\">Une urne contient des boules num\u00e9rot\u00e9es de 1 \u00e0 40. On en tire une au hasard, quelle est la probabilit\u00e9 que ce soit une boule portant un multiple de 3 impair ?<\/span><\/p>\n<p>R\u00e9ponse :<\/p>\n<p>On applique la formule ci-dessus :<\/p>\n<ul>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-series-lettres-nombres\/\">Nombre<\/a> total de cas : 40 (car 40 boules dans l\u2019urne).<\/li>\n<li>Nombre de cas favorables : les multiples de 3 qui sont impairs : 3 ; 9 ; 15 ; 21 ; 27 ; 33 ; 39. Il y en a 7.<\/li>\n<\/ul>\n<p>Donc la probabilit\u00e9 voulue vaut <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ddf4af86ea25d2227ea2bfb0a85e5f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#55;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/>.<\/p>\n<p>&nbsp;<\/p>\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\n<p>&nbsp;<\/p>\n<h2>Tirage sans remise en probabilit\u00e9s : Attention le total change !<\/h2>\n<p><em>Exemple type pour illustrer le tirage sans remise<\/em> :<\/p>\n<p>Une urne contient 4 boules rouges, 5 noires et 6 vertes. On tire au hasard et sans remise deux boules de l\u2019urne. Quelle est la probabilit\u00e9 d\u2019obtenir deux boules noires ?<\/p>\n<p><em>R\u00e9ponses<\/em> :<\/p>\n<p>Il faut bien comprendre qu\u2019on va multiplier les probabilit\u00e9s : celle d\u2019avoir une noire au 1er tirage avec celle d\u2019avoir une noire au 2nd tirage. Mais attention, pour le second tirage, la boule noire tir\u00e9e n\u2019a pas \u00e9t\u00e9 remise dans l\u2019urne.<\/p>\n<ul>\n<li>1er tirage : il y 15 boules au total et 5 noires, la probabilit\u00e9 d\u2019en tirer une vaut <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-81b66db3206a88063e7150353c383f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#53;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/li>\n<li>2nd tirage, il ne reste que 14 boules au total et plus que 4 noires, la probabilit\u00e9 d\u2019en tirer une vaut <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d7e3094c9905cbc1fbb9496cd70679a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#125;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/li>\n<\/ul>\n<p>Donc la probabilit\u00e9 de tirer deux boules noires vaut : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-81b66db3206a88063e7150353c383f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#53;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d7e3094c9905cbc1fbb9496cd70679a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#125;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/p>\n<p>On peut simplifier le calcul : <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-81b66db3206a88063e7150353c383f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#53;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-d7e3094c9905cbc1fbb9496cd70679a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#52;&#125;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e465b68a5e62695604eb3892d5dddf6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-139b2602c56735e0e72a35f829723765_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-38fde1dba92cf453d447897a3b2da314_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/>.<\/p>\n<h2>Obtenir au moins un&#8230; r\u00e9flexe \u00e0 avoir en probabilit\u00e9s !<\/h2>\n<p>Si dans un \u00e9nonc\u00e9, on lit : \u00ab au moins un\u2026 \u00bb, il faut penser \u00e0 prendre l\u2019\u00e9v\u00e9nement contraire :<\/p>\n<p>Si on note A un \u00e9v\u00e9nement et <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ed46621c8e86e9928a3cf0a340bfa33d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: 0px;\"\/> son contraire on a :<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-ba317f077b82cd37bf37c07286fdd3e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#65;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"38\" style=\"vertical-align: -5px;\"\/> = 1 &#8211; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8c9a50093749dca9f8dd1c76e178282b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#65;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"\/><\/p>\n<p>Dans cette classe, au moins un \u00e9l\u00e8ve aime les cours de maths. Le contraire de cette proposition est : dans cette classe, aucun \u00e9l\u00e8ve n\u2019aime les maths.<\/p>\n<p>Donc le contraire de <strong>au moins un fait<\/strong>\u2026 est <strong>personne ne fait<\/strong>\u2026Cette notion est \u00e0 ma\u00eetriser pour le sous test 3 du Tage Mage et \u00e9videmment pour le programme de maths de terminale.<\/p>\n<p><em>Exemple type pour illustrer<\/em> les \u00e9v\u00e9nements contraires :<\/p>\n<p>Une famille est compos\u00e9e de 3 enfants, quelle est la probabilit\u00e9 qu\u2019il y ait au moins une fille ?<\/p>\n<p><em>R\u00e9ponse<\/em> :<\/p>\n<p>Sans plus d\u2019indication, on prend pour vrai qu\u2019on a une chance sur deux d\u2019avoir un gar\u00e7on (ou une fille) \u00e0 la naissance.<\/p>\n<p>Le contraire d\u2019obtenir au moins une fille est : ne pas obtenir de fille, autrement dit avoir 3 gar\u00e7ons.<\/p>\n<p>On utilise la formule : P (au moins une fille) = 1 \u2013 P (aucune fille)<\/p>\n<p>Or la probabilit\u00e9 d\u2019avoir un gar\u00e7on vaut 1\/2, donc d\u2019en avoir 3 :<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-734ff31239bb98fa2778b5856779f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-734ff31239bb98fa2778b5856779f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-5aa3fe0ad89cf65f34b5c880c078356e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-66458010f3eecf6eb46831af8c0845d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p>Et donc la probabilit\u00e9 d\u2019avoir au moins une fille vaut :<\/p>\n<p><strong>1 &#8211;<\/strong> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-66458010f3eecf6eb46831af8c0845d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-cf821a20d722879f4d5f734531d4bca7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#56;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> &#8211; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-e325fb0686212dcd42f7e6d33c9bb01e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-602b5c844f1c5d7cf2b0064a590d2788_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<h2>Union et Intersection en probabilit\u00e9s :\u00a0 cours<\/h2>\n<p>L\u2019union \u222a signifie : ou (non exclusif) c&rsquo;est-\u00e0-dire soit l\u2019un, soit l\u2019autre, soit les deux. C\u2019est un et\/ou.<\/p>\n<p>L\u2019intersection \u2229 signifie : et dans le sens de : \u00e0 la fois, simultan\u00e9ment, ce qu\u2019il y a en commun.<\/p>\n<p><strong>Formules de proba : L&rsquo;union et l&rsquo;intersection<\/strong><\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-58a7e378f2e3c80e8b543690602d01cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#65;&#32;&#92;&#99;&#117;&#112;&#32;&#66;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8c9a50093749dca9f8dd1c76e178282b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#65;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"\/> + <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-350339fac6e82610dfe4051b77a7c336_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#66;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"39\" style=\"vertical-align: -5px;\"\/> &#8211; <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-55b60dfad205fcf856f5040af262b61d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#65;&#32;&#92;&#99;&#97;&#112;&#32;&#66;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"\/><\/p>\n<p>Ces formules de probabilit\u00e9s se visualisent \u00e0 l\u2019aide du diagramme de Venn qui \u00e9galement utilis\u00e9 sur les ensembles dans le programme de maths de seconde:<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-55736 size-full\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/06\/Diagramme-Venn.jpg\" alt=\"probabilit\u00e9s cours\" width=\"400\" height=\"158\" \/><\/p>\n<p>En fonc\u00e9e, la partie repr\u00e9sentant l\u2019intersection donc A\u2229B.<\/p>\n<p><em>Exemple type sur les intersections et les unions pour illustrer<\/em> :<\/p>\n<p>Dans un coll\u00e8ge de 450 \u00e9l\u00e8ves, on sait que 200 \u00e9l\u00e8ves prennent des <a href=\"https:\/\/groupe-reussite.fr\/cours-particuliers\/maths\/tous-niveaux\/france\/\">cours particuliers de math\u00e9matiques<\/a>, 150 font des cours particuliers de fran\u00e7ais et 50 font les deux. On choisit un \u00e9l\u00e8ve au hasard, quelle est la probabilit\u00e9 qu\u2019il fasse des cours particuliers en maths ou des cours particuliers en fran\u00e7ais ?<\/p>\n<p>R\u00e9ponse : la r\u00e9ponse n\u2019est pas 400\/450 !<\/p>\n<p>200 \u00e9l\u00e8ves font des cours particuliers en maths, mais ils peuvent aussi faire des cours particuliers en fran\u00e7ais: aucune contre indication.<\/p>\n<p>Sinon on aurait eu : \u00ab 200 \u00e9l\u00e8ves font uniquement des cours particuliers de maths\u00bb<\/p>\n<p>Idem pour les 150 qui prennent des cours de fran\u00e7ais, certains prennent des cours de maths.<\/p>\n<p>La seule chose dont on est s\u00fbr : 50 \u00e9l\u00e8ves prennent les deux mati\u00e8res donc :<\/p>\n<ul>\n<li>200 \u2013 50 = 150 \u00e9l\u00e8ves prennent uniquement des cours de maths<\/li>\n<li>150 \u2013 50 = 100 \u00e9l\u00e8ves prennent uniquement des cours de fran\u00e7ais<\/li>\n<\/ul>\n<p>Nombre d\u2019\u00e9l\u00e8ves qui font des cours de maths ou des cours de fran\u00e7ais :<\/p>\n<p>Ceux qui font que des cours de maths + ceux qui font que des cours de fran\u00e7ais + ceux qui font les deux.<\/p>\n<p>Soit : 150 +100 + 50 = 300 \u00e9l\u00e8ves. Et donc la probabilit\u00e9 cherch\u00e9e vaut 300\/450 soit 2\/3.<\/p>\n<p>&nbsp;<\/p>\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\n<p>&nbsp;<\/p>\n<h2>Arbre de probabilit\u00e9s cours<\/h2>\n<p>Il faut en faire quelques-uns pour que leur maniement devienne fluide et comprendre quand il faut les utiliser ou alors avoir de bons souvenirs du programme de maths de 1\u00e8re et Terminale.<br \/>\nSe souvenir :<\/p>\n<ul>\n<li>Quand on veut tout un chemin (une intersection \u2229), on multiplie les probabilit\u00e9s.<\/li>\n<li>Si plusieurs chemins conviennent, on les additionne.<\/li>\n<\/ul>\n<p><em>Exemple type pour illustrer les arbres en probabilit\u00e9s :<\/em><\/p>\n<p>Un groupe est constitu\u00e9 aux trois quarts de gar\u00e7ons. On sait de plus que la moiti\u00e9 des gar\u00e7ons aime les maths contre 60% des filles. On choisit une personne du groupe au hasard, quelle est la probabilit\u00e9 qu\u2019elle aime les maths ?<\/p>\n<p><em>R\u00e9ponse :<\/em><\/p>\n<p>Quand on construit un arbre, il y a une forme de chronologie. Ici :<\/p>\n<ul>\n<li>D\u2019abord on est un gar\u00e7on ou une fille,<\/li>\n<li>puis on aime les maths ou pas<\/li>\n<\/ul>\n<p>Le squelette de l\u2019arbre est le suivant :<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-55864 size-full\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/06\/arbe-probabilite.jpg\" alt=\"probabilit\u00e9s cours\" width=\"407\" height=\"205\" \/><\/p>\n<p>On le compl\u00e8te alors :<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-55740 size-full\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/uploads\/2020\/06\/Arbre-pourcentage-probabilite.jpg\" alt=\"probabilit\u00e9s cours\" width=\"486\" height=\"221\" \/><\/p>\n<p>Pour les calculs, il faudra \u00eatre coh\u00e9rent : soit uniquement des <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-fractions\/\">fractions<\/a> soit des <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-pourcentages\/\">pourcentages<\/a>. On privil\u00e9gie les fractions quasi exclusivement.<\/p>\n<p>On cherche la probabilit\u00e9 que la personne aime les maths. Il y a 2 possibilit\u00e9s :<\/p>\n<ul>\n<li>Soit cette personne aime les maths en \u00e9tant un gar\u00e7on (G\u2229M) soit <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-88c4bfafbe671f6c6f9286457e82fa15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -13px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-734ff31239bb98fa2778b5856779f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/li>\n<li>Soit cette personne aime les maths en \u00e9tant une fille (F\u2229M) soit\u00a0 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-fec3a9d3b8444d728f2d9088ba1f3f5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -13px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f14b6e3ebcc34861577ca55cb2411e98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"27\" style=\"vertical-align: -13px;\"\/> (et\u00a0 <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-f14b6e3ebcc34861577ca55cb2411e98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#54;&#48;&#125;&#123;&#49;&#48;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"27\" style=\"vertical-align: -13px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-c16d8cdbd1c056927e05c951512c21de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#54;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -13px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1c6ec3ba87a081f996bc355af2d1214c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/>)<\/li>\n<\/ul>\n<p>Il y a donc deux chemins qui nous conviennent, on additionne \u00ab ces chemins \u00bb, donc les probabilit\u00e9s trouv\u00e9es, apr\u00e8s les avoir simplifi\u00e9es.<\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-abb8f63868e3d4fd841de971dd770122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#77;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-88c4bfafbe671f6c6f9286457e82fa15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -13px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-734ff31239bb98fa2778b5856779f79a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> + <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-fec3a9d3b8444d728f2d9088ba1f3f5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -13px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-3e2a3b7b9d8913e71519bf7df9eb51b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#105;&#109;&#101;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"\/> <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-1c6ec3ba87a081f996bc355af2d1214c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/><\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-abb8f63868e3d4fd841de971dd770122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#80;&#125;&#40;&#77;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-b95fa2815f84469f5877e9aac5a8e4f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\"\/> + <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-2d8f0b3db951c0907cf5511b84d6b5a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#51;&#125;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-8e4c5f798ee6dcec91ceebb1fd764e17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#49;&#53;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"18\" style=\"vertical-align: -12px;\"\/> + <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-89b3ee2239a32ad2f5543baafa1aba5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#54;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/> = <img loading=\"lazy\" src=\"https:\/\/groupe-reussite.fr\/ressources\/wp-content\/ql-cache\/quicklatex.com-cbcb42439baa8f3cdf596b790856d0a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#32;&#123;&#50;&#49;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"18\" style=\"vertical-align: -12px;\"\/><\/p>\n<p>Donc la probabilit\u00e9 que la personne aime les maths est de 21\/40.<\/p>\n<p style=\"text-align: justify\">Dans la pr\u00e9paration du Tage Mage ou dans la pr\u00e9paration du Gmat ou m\u00eame du Score IAE Message en vue d&rsquo;entrer dans les meilleures \u00e9coles de commerce, les probabilit\u00e9s et le <a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-denombrement\/\">d\u00e9nombrement<\/a> occupent une bonne place dans les \u00e9preuves qui permettent de s\u00e9lectionner les candidats. Cependant, d&rsquo;autres cours sont \u00e9galement fondamentaux pour r\u00e9ussir le Tage Mage et plus particuli\u00e8rement le sous-test 2, notamment :<\/p>\n<ul style=\"text-align: justify\">\n<li style=\"text-align: justify\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-moyenne-arithmetique-moyenne-ponderee\/\">Cours sur les moyennes Tage Mage<\/a><\/li>\n<li style=\"text-align: justify\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-pythagore\/\">R\u00e9sum\u00e9 de cours sur th\u00e9or\u00e8me de Pythagore Tage Mage<\/a><\/li>\n<li style=\"text-align: justify\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-theoreme-de-thales\/\">Fiche de r\u00e9vision th\u00e9or\u00e8me de Thal\u00e8s au Tage Mage<\/a><\/li>\n<li style=\"text-align: justify\"><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-racines-carrees\/\">R\u00e9vision sur les racines carr\u00e9es au Tage Mage<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-probabilites\/\">Exercices corrig\u00e9s Probabilit\u00e9s au Tage Mage<\/a><\/li>\n<li><a href=\"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-moyenne-arithmetique-moyenne-ponderee\/\">Entra\u00eenement sur les moyennes au Tage Mage<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Probabilit\u00e9 : cours et formules de probabilit\u00e9 de base R\u00e9sum\u00e9 de cours Exercices et corrig\u00e9s Cours en ligne du Tage Mage Les probabilit\u00e9s accompagnent les \u00e9l\u00e8ves tout au long de leur scolarit\u00e9, du coll\u00e8ge \u00e0 la pr\u00e9paration du bac pour certains, mais aussi jusqu&rsquo;en pr\u00e9pa et pas uniquement en MPSI ou PCSI et pr\u00e9pa HEC. [&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>Probabilit\u00e9s cours et formules de probabilit\u00e9s de base<\/title>\n<meta name=\"description\" content=\"Probabilit\u00e9s cours sur les probabilit\u00e9s avec les fondamentaux et les formules proba de base pour mieux comprendre la logique derri\u00e8re.\" \/>\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-probabilites\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probabilit\u00e9s cours et formules de probabilit\u00e9s de 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