{"id":2884,"date":"2023-12-06T21:09:13","date_gmt":"2023-12-06T20:09:13","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2884"},"modified":"2025-12-05T12:54:12","modified_gmt":"2025-12-05T11:54:12","slug":"la-fourmi","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2884","title":{"rendered":"La fourmi"},"content":{"rendered":"\r\n<h2>\u00c9nonc\u00e9 du probl\u00e8me<\/h2>\r\n<p>Une fourmi peut rentrer ou sortir dans un pi\u00e8ge par le point A. Quand elle est \u00e0 un sommet, elle choisit au hasard une des trois ar\u00eates qui passent par ce sommet.<\/p>\r\n<p>La fourmi est vivante si elle retourne au point A en ayant parcouru au plus 4 ar\u00eates.<\/p>\r\n<p>Sa chance de survie est-elle sup\u00e9rieur ou inf\u00e9rieure \u00e0 une chance sur deux ?<br \/>Essaye d&rsquo;estimer sa chance de survie.<\/p>\r\n<h3>Variante :<\/h3>\r\n<p>On peut choisir un autre poly\u00e8dre sur lequel se d\u00e9placerait la fourmi.<\/p>\r\n<p><img loading=\"lazy\" decoding=\"async\" title=\"FourmiIllustration\" src=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png\" alt=\"FourmiIllustration\" width=\"283\" height=\"276\" \/> <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=79\" target=\"_self\"> Retour Panier \u00e0 probl\u00e8mes <\/a><\/p>\r\n<h2>Au cycle 3<\/h2>\r\n<p>Bien que les probabilit\u00e9s ne soient pas au programme du cycle 3, on visera plut\u00f4t \u00e0 travers ce probl\u00e8me la repr\u00e9sentation d&rsquo;une situation par un arbre<\/p>\r\n<h3>Comp\u00e9tences transversales<\/h3>\r\n<p>\u2666 Former les \u00e9l\u00e8ves \u00e0 la pens\u00e9e statistique et aux ph\u00e9nom\u00e8nes al\u00e9atoires.<br \/>\u2666 Construire des outils de synth\u00e8se (tableaux, arbres, pourcentages, fr\u00e9quences).<br \/>\u2666 Construire des outils de repr\u00e9sentation (diagrammes et graphiques divers).<br \/>\u2666 Construire des caract\u00e8res de position d&rsquo;une s\u00e9rie statistique (moyenne, m\u00e9diane. . .).<\/p>\r\n<h3>Connaissances math\u00e9matiques<\/h3>\r\n<p>\u2666 Calculer des fr\u00e9quences ou des pourcentages.<br \/>\u2666 D\u00e9nombrer.<br \/>\u2666 Calculer une probabilit\u00e9.<br \/>\u2666 Utiliser la notion de fraction. <a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/12\/DREAM_NarrationRecherche_La-Fourmi.pdf\" target=\"_blank\" rel=\"noopener\"> T\u00e9l\u00e9charcher le document complet <\/a><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Une fourmi part du point A et se d\u00e9place au hasard sur un graphe. Sa survie d\u00e9pend-elle de revenir \u00e0 A en quatre ar\u00eates maximum\u202f? Quelle est sa probabilit\u00e9\u202f?<\/p>\n","protected":false},"author":3,"featured_media":2521,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107],"tags":[],"niveau":[113],"type_situation":[116],"theme_maths":[118,119],"probleme_associe":[138],"type-expe":[],"class_list":{"0":"post-2884","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-situation-probleme","8":"niveau-cycle-4","9":"type_situation-situation-probleme","10":"theme_maths-nombres-et-calculs","11":"theme_maths-ogd-fonctions","12":"probleme_associe-la-fourmi","13":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration-150x150.png",150,150,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration-270x250.png",270,250,true],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration-283x200.png",283,200,true],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration-283x200.png",283,200,true],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration.png",283,276,false],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/02\/FourmiIllustration-283x94.png",283,94,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=107\" rel=\"category\">Situation Probl\u00e8me<\/a>","rttpg_excerpt":"Une fourmi part du point A et se d\u00e9place au hasard sur un graphe. Sa survie d\u00e9pend-elle de revenir \u00e0 A en quatre ar\u00eates maximum\u202f? Quelle est sa probabilit\u00e9\u202f?","_links":{"self":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2884","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=2884"}],"version-history":[{"count":12,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2884\/revisions"}],"predecessor-version":[{"id":3812,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2884\/revisions\/3812"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/media\/2521"}],"wp:attachment":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2884"},{"taxonomy":"niveau","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fniveau&post=2884"},{"taxonomy":"type_situation","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype_situation&post=2884"},{"taxonomy":"theme_maths","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftheme_maths&post=2884"},{"taxonomy":"probleme_associe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fprobleme_associe&post=2884"},{"taxonomy":"type-expe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype-expe&post=2884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}