{"id":26691,"date":"2021-04-04T13:00:34","date_gmt":"2021-04-04T13:00:34","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=26691"},"modified":"2024-05-21T11:47:33","modified_gmt":"2024-05-21T11:47:33","slug":"fondements-des-probabilites-et-problemes-pratiques","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/fondements-des-probabilites-et-problemes-pratiques\/","title":{"rendered":"Fondements des Probabilit\u00e9s et Probl\u00e8mes Pratiques"},"content":{"rendered":"<div style=\"background-color:#F3F3F3; padding:20px;\">\n<center><\/p>\n<h1>Probl\u00e8mes Pratiques avec les Concepts Fondamentaux des Probabilit\u00e9s<\/h1>\n<p><\/p>\n<p style=\"text-align:center;\"><strong>R\u00e9sum\u00e9<\/strong><br \/><em> Dans cette classe, nous examinerons des exercices pratiques tels que la fiabilit\u00e9 d&#8217;un syst\u00e8me de contr\u00f4le, des strat\u00e9gies de jeux de cartes et des calculs de probabilit\u00e9s dans des situations quotidiennes. Les solutions aux probl\u00e8mes sont pr\u00e9sent\u00e9es en vid\u00e9o, ce qui vous permettra de renforcer votre compr\u00e9hension et vos comp\u00e9tences dans le domaine des probabilit\u00e9s en comparant vos d\u00e9veloppements et en analysant les n\u00f4tres.<\/em><\/p>\n<p><\/center><br \/>\n<\/p>\n<p style=\"text-align:center;\"><strong>OBJECTIFS D&#8217;APPRENTISSAGE:<\/strong><br \/>\n\u00c0 la fin de cette classe, l&#8217;\u00e9tudiant sera capable de:\n<\/p>\n<ol>\n<li><strong>R\u00e9soudre<\/strong> des probl\u00e8mes impliquant des \u00e9l\u00e9ments de base des probabilit\u00e9s<\/li>\n<\/ol>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/5TqlIRqwyRA\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center>\n<\/div>\n<p style=\"text-align: justify; color: #000000;\">\u00c0 ce stade, il est n\u00e9cessaire de faire quelques exercices pratiques impliquant les id\u00e9es de base des probabilit\u00e9s [<a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-el-espacio-muestral\/\" rel=\"noopener\" target=\"_blank\">1<\/a>,<a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-eventos-y-la-sigma-algebra\/\" rel=\"noopener\" target=\"_blank\">2<\/a>,<a href=\"https:\/\/toposuranos.com\/el-espacio-de-probabilidades-medida-de-probabilidad\/\" rel=\"noopener\" target=\"_blank\">3<\/a>]. Le conseil, comme toujours, est : essayez d&#8217;abord de r\u00e9soudre ces exercices de probabilit\u00e9s par vous-m\u00eame, puis regardez la vid\u00e9o pour comparer et corriger vos r\u00e9sultats.<\/p>\n<ol style=\"text-align: justify; color: #000000;\">\n<li>Un syst\u00e8me de contr\u00f4le est compos\u00e9 de 10 composants. La d\u00e9faillance de l&#8217;un d&#8217;eux peut provoquer la d\u00e9faillance du syst\u00e8me complet. Il est connu que la probabilit\u00e9 de d\u00e9faillance de chaque composant est <span class=\"katex-eq\" data-katex-display=\"false\">\\leq 0,0002.<\/span> Prouvez que la probabilit\u00e9 que le syst\u00e8me fonctionne correctement est <span class=\"katex-eq\" data-katex-display=\"false\">\\geq 0,998.<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=5TqlIRqwyRA&amp;t=42s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[SOLUTION]<\/span><\/strong><\/a><\/li>\n<li>Sur une table, il y a trois cartes face cach\u00e9e : un \u00abas\u00bb et deux \u00abjokers\u00bb. Le jeu consiste \u00e0 deviner laquelle des cartes est un as. Vous en choisissez une et \u00e0 ce moment-l\u00e0, le croupier vous montre une des deux autres cartes, qui se r\u00e9v\u00e8le \u00eatre un \u00abjoker\u00bb, et vous donne l&#8217;opportunit\u00e9 de changer votre choix. Qu&#8217;est-ce qui est mieux : maintenir ou changer votre choix pour l&#8217;autre carte inconnue ? <a href=\"https:\/\/www.youtube.com\/watch?v=5TqlIRqwyRA&amp;t=368s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><\/li>\n<li>Cas d&#8217;une erreur en additionnant les probabilit\u00e9s : <a href=\"https:\/\/www.youtube.com\/watch?v=5TqlIRqwyRA&amp;t=600s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[SOLUTION]<\/span><\/strong><\/a>\n<ul>\n<li><strong>Cas 1:<\/strong> Il y a deux paniers, un rouge et un blanc. Le panier rouge contient 5 pi\u00e8ces d&#8217;or et 6 de fer-blanc, tandis que le panier blanc en contient 3 en or et 4 en fer-blanc. De quel panier est-il pr\u00e9f\u00e9rable de tirer une pi\u00e8ce ?<\/li>\n<li><strong>Cas 2:<\/strong> Comme dans le cas pr\u00e9c\u00e9dent, il y a deux paniers, un rouge et un blanc. Le panier rouge contient 6 pi\u00e8ces d&#8217;or et 3 de fer-blanc, tandis que le panier blanc en contient 9 en or et 5 en fer-blanc. De quel panier est-il pr\u00e9f\u00e9rable de tirer une pi\u00e8ce ?<\/li>\n<li><strong>Cas 3:<\/strong> Maintenant, le contenu des deux paniers rouges pr\u00e9c\u00e9dents est combin\u00e9 en un seul et grand panier rouge, et il en va de m\u00eame pour les paniers blancs des deux cas pr\u00e9c\u00e9dents. La tendance observ\u00e9e dans les cas pr\u00e9c\u00e9dents se maintiendra-t-elle ?<\/li>\n<\/ul>\n<p>&nbsp;<\/li>\n<li>Un magasin \u00e9met des tickets de service de 5 chiffres. Si vous tirez un ticket au hasard, quelle est la probabilit\u00e9 qu&#8217;il soit un palindrome ? NOTE : Un palindrome est un nombre qui se lit de la m\u00eame mani\u00e8re de l&#8217;avant vers l&#8217;arri\u00e8re ; par exemple : 13431 est un palindrome. <a href=\"https:\/\/www.youtube.com\/watch?v=5TqlIRqwyRA&amp;t=837s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><\/li>\n<li>Un d\u00e9 \u00e9quilibr\u00e9 \u00e0 6 faces est lanc\u00e9 de mani\u00e8re r\u00e9p\u00e9t\u00e9e. Calculez la probabilit\u00e9 d&#8217;obtenir : <a href=\"https:\/\/www.youtube.com\/watch?v=5TqlIRqwyRA&amp;t=1038s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><br \/>\na) Deux nombres pairs, en lan\u00e7ant deux fois.<br \/>\nb) Au moins un as en lan\u00e7ant 4 fois.<\/li>\n<li>Cinq d\u00e9s \u00e9quilibr\u00e9s \u00e0 6 faces sont lanc\u00e9s. Calculez la probabilit\u00e9 d&#8217;obtenir : <a href=\"https:\/\/www.youtube.com\/watch?v=5TqlIRqwyRA&amp;t=2161s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><br \/>\na) Cinq nombres identiques<br \/>\nb) Quatre identiques et un diff\u00e9rent<br \/>\nc) Trois d&#8217;un nombre et deux d&#8217;un autre<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Probl\u00e8mes Pratiques avec les Concepts Fondamentaux des Probabilit\u00e9s R\u00e9sum\u00e9 Dans cette classe, nous examinerons des exercices pratiques tels que la fiabilit\u00e9 d&#8217;un syst\u00e8me de contr\u00f4le, des strat\u00e9gies de jeux de cartes et des calculs de probabilit\u00e9s dans des situations quotidiennes. Les solutions aux probl\u00e8mes sont pr\u00e9sent\u00e9es en vid\u00e9o, ce qui vous permettra de renforcer votre [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":26402,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":4,"footnotes":""},"categories":[569,682],"tags":[],"class_list":["post-26691","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematiques","category-probabilites-et-statistiques"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Fondements des Probabilit\u00e9s et Probl\u00e8mes Pratiques - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Explorez ces probl\u00e8mes pratiques sur les probabilit\u00e9s et ma\u00eetrisez les concepts de base pour am\u00e9liorer vos comp\u00e9tences en prise de d\u00e9cision.\" \/>\n<meta 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