{"id":3433,"date":"2023-12-01T20:01:24","date_gmt":"2023-12-01T19:01:24","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=3433"},"modified":"2026-04-27T12:44:32","modified_gmt":"2026-04-27T10:44:32","slug":"les-urnes-de-polya","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=3433","title":{"rendered":"Les urnes de Polya"},"content":{"rendered":"\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/\">Accueil<\/a> \u00bb <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=3328\">Ressources p\u00e9dagogiques<\/a> \u00bb <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=77\">Des exemples de SDRP<\/a> \u00bb Les urnes de Polya<\/p>\r\n<h1>L&rsquo;\u00e9nonc\u00e9 de la situation<\/h1>\r\n<p>Une urne contient une boule blanche et une boule rouge.<\/p>\r\n<p>On tire une boule au hasard et on replace dans l&rsquo;urne la boule choisie et une autre boule de la m\u00eame couleur.<\/p>\r\n<p>On s&rsquo;int\u00e9resse\u00a0\u00e0 la composition de l&rsquo;urne lorsque l&rsquo;on recommence le tirage n fois de suite.<\/p>\r\n<p>Vid\u00e9o en construction<\/p>\r\n<h1>Les math\u00e9matiques en jeu<\/h1>\r\n<ul>\r\n<li>Echantillon<\/li>\r\n<li>Fr\u00e9quence<\/li>\r\n<li>Fluctuation<\/li>\r\n<li>Simulation<\/li>\r\n<li>Probabilit\u00e9, loi de probabilit\u00e9, probabilit\u00e9 conditionnelle.<\/li>\r\n<li>Arbres<\/li>\r\n<li>Variable al\u00e9atoire<\/li>\r\n<\/ul>\r\n<h4>Analyse math\u00e9matique<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/UrnesPlya_Analyse_Maths_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h4>Analyse didactique<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/UrnesPolya_Analyse_didactique_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h4>Exemples de mise en \u0153uvre<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/UrnesPolya_Mise_en_oeuvre_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n<h4>Pour aller plus loin<\/h4>\r\n<p><a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/04\/UrnesPolya_Aller_Plus_Loin_DREAM.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charger le document <\/a><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Une urne contient une boule blanche et une rouge. \u00c0 chaque tirage, on replace la boule tir\u00e9e et on en ajoute une de m\u00eame couleur. Comment \u00e9volue la composition de l\u2019urne apr\u00e8s n tirages ?<\/p>\n","protected":false},"author":3,"featured_media":2491,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[106],"tags":[],"niveau":[113,114],"type_situation":[115],"theme_maths":[119],"probleme_associe":[129],"type-expe":[],"class_list":{"0":"post-3433","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-sdrp","8":"niveau-cycle-4","9":"niveau-lycee","10":"type_situation-sdrp","11":"theme_maths-ogd-fonctions","12":"probleme_associe-les-urnes-de-polya","13":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1-150x150.png",150,150,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1-300x142.png",300,142,true],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1-270x184.png",270,184,true],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1.png",389,184,false],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/UrnesPolyaBouton-1-389x94.png",389,94,true]},"rttpg_author":{"display_name":"St\u00e9phanie CROQUELOIS","author_link":"https:\/\/math.univ-lyon1.fr\/dream\/?author=3"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?cat=106\" rel=\"category\">SDRP<\/a>","rttpg_excerpt":"Une urne contient une boule blanche et une rouge. \u00c0 chaque tirage, on replace la boule tir\u00e9e et on en ajoute une de m\u00eame couleur. Comment \u00e9volue la composition de l\u2019urne apr\u00e8s n tirages ?","_links":{"self":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/3433","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3433"}],"version-history":[{"count":7,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/3433\/revisions"}],"predecessor-version":[{"id":3779,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/3433\/revisions\/3779"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/media\/2491"}],"wp:attachment":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3433"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3433"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3433"},{"taxonomy":"niveau","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fniveau&post=3433"},{"taxonomy":"type_situation","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype_situation&post=3433"},{"taxonomy":"theme_maths","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftheme_maths&post=3433"},{"taxonomy":"probleme_associe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fprobleme_associe&post=3433"},{"taxonomy":"type-expe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype-expe&post=3433"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}