{"id":7211,"date":"2011-11-27T18:58:25","date_gmt":"2011-11-27T18:58:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7211"},"modified":"2022-01-25T22:50:05","modified_gmt":"2022-01-25T22:50:05","slug":"um-autocarro-chega-a-fronteira","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7211","title":{"rendered":"Um autocarro chega \u00e0 fronteira"},"content":{"rendered":"<p><ul id='GTTabs_ul_7211' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7211' class='GTTabs_curr'><a  id=\"7211_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7211' ><a  id=\"7211_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_7211'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/mercedes-benz2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7212\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7212\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/mercedes-benz2.jpg\" data-orig-size=\"248,143\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Autocarro\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/mercedes-benz2.jpg\" class=\"alignright size-full wp-image-7212\" title=\"Autocarro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/mercedes-benz2.jpg\" alt=\"\" width=\"248\" height=\"143\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/mercedes-benz2.jpg 248w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/mercedes-benz2-150x86.jpg 150w\" sizes=\"auto, (max-width: 248px) 100vw, 248px\" \/><\/a>Um autocarro chega \u00e0 fronteira com 30 passageiros. Destes 30 passageiros, 10 levam contrabando.<\/p>\n<p>O funcion\u00e1rio da alf\u00e2ndega vai vistoriar 8 passageiros escolhidos ao acaso.<\/p>\n<p>Qual \u00e9 a probabilidade de dois e s\u00f3 dois dos passageiros com contrabando sejam escolhidos? (Apresente o resultado aproximado \u00e0s mil\u00e9simas.)<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7211' onClick='GTTabs_show(1,7211)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7211'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>\u00a0Existem ${}^{30}{{C}_{8}}$ maneiras distintas de escolher 8 dos 30 passageiros.<\/p>\n<p>Destas, h\u00e1 apenas ${}^{10}{{C}_{2}}\\times {}^{20}{{C}_{6}}$ em que esse grupo \u00e9 constitu\u00eddo por dois passageiros com contrabando e seis sem contrabando.<\/p>\n<p>Logo, a probabilidade pedida \u00e9 $$p=\\frac{{}^{10}{{C}_{2}}\\times {}^{20}{{C}_{6}}}{{}^{30}{{C}_{8}}}=\\frac{45\\times 38760}{5852925}=\\frac{2584}{8671}\\approx 0,298$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7211' onClick='GTTabs_show(0,7211)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um autocarro chega \u00e0 fronteira com 30 passageiros. Destes 30 passageiros, 10 levam contrabando. O funcion\u00e1rio da alf\u00e2ndega vai vistoriar 8 passageiros escolhidos ao acaso. Qual \u00e9 a probabilidade de dois&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255],"series":[],"class_list":["post-7211","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-aplicando","category-probabilidades-e-combinatoria","tag-12-o-ano","tag-analise-combinatoria"],"views":2724,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag175-51_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7211","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=7211"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7211\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21040"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7211"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7211"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7211"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7211"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}