{"id":2379,"date":"2019-09-02T10:56:00","date_gmt":"2019-09-02T06:56:00","guid":{"rendered":"https:\/\/iremi.univ-reunion.fr\/?p=2379"},"modified":"2026-09-06T11:21:59","modified_gmt":"2026-09-06T07:21:59","slug":"un-jeu-pour-les-probabilites-conditionnelles","status":"publish","type":"post","link":"https:\/\/iremi.univ-reunion.fr\/?p=2379","title":{"rendered":"Un jeu pour les probabilit\u00e9s conditionnelles"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Les probabilit\u00e9s conditionnelles apparaissent dans le programme de math\u00e9matiques de Seconde \u00e0 la rentr\u00e9e 2026. C&rsquo;est l&rsquo;occasion pour y pratiquer le jeu pr\u00e9sent\u00e9 ici, et qui a fait l&rsquo;objet de s\u00e9ances en BTS (sur les probabilit\u00e9s conditionnelles). L&rsquo;activit\u00e9 provient de <a href=\"https:\/\/www.editions-ellipses.fr\/fr\/accueil\/15759-jeux-et-graphes-la-theorie-des-graphes-de-5-a-95-ans-2e-edition-9782340101494.html\">ce livre<\/a> (chapitre 3 : arbres pond\u00e9r\u00e9s). <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Voici le plateau de jeu :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2026\/08\/arbre2.pdf\" type=\"application\/pdf\" style=\"width:100%;height:960px\" aria-label=\"Contenu embarqu\u00e9 arbre2.\"><\/object><a id=\"wp-block-file--media-b101ca31-d839-48d0-b4ac-88abb78801e6\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2026\/08\/arbre2.pdf\">arbre2<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2026\/08\/arbre2.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-b101ca31-d839-48d0-b4ac-88abb78801e6\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Il s&rsquo;agit d&rsquo;un jeu \u00e0 deux joueurs appel\u00e9s A et B. Pour tout couple de joueurs, il faut un d\u00e9 et un pion (commun aux deux joueurs). Les joueurs chacun son tour<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>lancent le d\u00e9<\/li>\n\n\n\n<li>d\u00e9placent le pion suivant la face sortie.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Quand le pion est arriv\u00e9 au bout, il se trouve sur une feuille de l&rsquo;arbre. La lettre \u00e9crite sur cette feuille indique le nom du gagnant.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La question est de savoir si le jeu est \u00e9quitable, et pour cela il faut jouer un grand nombre de fois et noter l&rsquo;identit\u00e9 (A ou B) du gagnant. En fin de s\u00e9ance, on peut calculer la probabilit\u00e9 de gain de chacun des joueurs, et v\u00e9rifier si les statistiques relev\u00e9es y sont conformes.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Voici un autre plateau de jeu, il est moins \u00e9quitable que l&rsquo;autre jeu et du coup, le but de l&rsquo;exercice est de regarder de combien A est avantag\u00e9 :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2026\/08\/arbre0.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 arbre0.\"><\/object><a id=\"wp-block-file--media-4accb95a-a26a-4ae5-a39c-425b2703dc3a\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2026\/08\/arbre0.pdf\">arbre0<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2026\/08\/arbre0.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4accb95a-a26a-4ae5-a39c-425b2703dc3a\">T\u00e9l\u00e9charger<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Les probabilit\u00e9s conditionnelles apparaissent dans le programme de math\u00e9matiques de Seconde \u00e0 la rentr\u00e9e 2026. C&rsquo;est l&rsquo;occasion pour y pratiquer le jeu pr\u00e9sent\u00e9 ici, et qui a fait l&rsquo;objet de s\u00e9ances en BTS (sur les probabilit\u00e9s conditionnelles). L&rsquo;activit\u00e9 provient de ce livre (chapitre 3 : arbres pond\u00e9r\u00e9s). Voici le plateau de jeu : Il s&rsquo;agit [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12,8],"tags":[32,48],"coauthors":[54],"class_list":["post-2379","post","type-post","status-publish","format-standard","hentry","category-jeux-mathematiques","category-probabilites","tag-lycee","tag-manipulation"],"_links":{"self":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/2379","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2379"}],"version-history":[{"count":2,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/2379\/revisions"}],"predecessor-version":[{"id":2383,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/2379\/revisions\/2383"}],"wp:attachment":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2379"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2379"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2379"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcoauthors&post=2379"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}