{"id":6942,"date":"2011-09-29T00:57:14","date_gmt":"2011-09-28T23:57:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6942"},"modified":"2022-01-16T02:47:55","modified_gmt":"2022-01-16T02:47:55","slug":"a-turma-da-maria-jose","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6942","title":{"rendered":"A turma da Maria Jos\u00e9"},"content":{"rendered":"<p><ul id='GTTabs_ul_6942' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6942' class='GTTabs_curr'><a  id=\"6942_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6942' ><a  id=\"6942_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_6942'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Foi feito um inqu\u00e9rito aos 28 alunos da turma da Maria Jos\u00e9 sobre os desportos que praticavam.<\/p>\n<p>Concluiu-se que 15 praticavam futebol e 16 basquetebol. (Qualquer aluno da turma pratica pelo menos uma dessas modalidades.)<\/p>\n<p>\u00a0Qual \u00e9 a probabilidade de, escolhido um aluno da turma ao acaso, ele praticar:<\/p>\n<ol>\n<li>futebol e basquetebol?<\/li>\n<li>futebol mas n\u00e3o basquetebol?<\/li>\n<li>basquetebol mas n\u00e3o futebol?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6942' onClick='GTTabs_show(1,6942)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6942'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Sejam T, F e B, respetivamente, o conjunto dos alunos da turna, o conjunto dos alunos que praticam futebol e o conjunto dos alunos que praticam basquetebol.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6943\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6943\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB.jpg\" data-orig-size=\"317,203\" 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=\"Diagrama\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB.jpg\" class=\"alignright size-full wp-image-6943\" title=\"Diagrama\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB.jpg\" alt=\"\" width=\"317\" height=\"203\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB.jpg 317w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB-300x192.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/DiagramaFB-150x96.jpg 150w\" sizes=\"auto, (max-width: 317px) 100vw, 317px\" \/><\/a>Ora, sabe-se que:<\/p>\n<ul>\n<li>A turma tem 28 alunos, logo $\\#T=28$;<\/li>\n<li>15 alunos praticam futebol, logo $\\#F=15$;<\/li>\n<li>16 alunos praticam basquetebol, logo $\\#B=16$.<\/li>\n<\/ul>\n<p>Como qualquer aluno da turma pratica pelo menos uma dessas modalidades e $\\#F+\\#B+0=15+16=31$, conclui-se que 3 alunos praticam as duas modalidades, isto \u00e9,\u00a0$\\#(F\\cap B)=3$.<\/p>\n<p>Esta conclus\u00e3o conjuntamente com os dados do problema permitem elaborar o diagrama apresentado ao lado.<\/p>\n<ol>\n<li>Logo, $P(\\text{&#8221;praticar futebol e basquetebol&#8221;})=\\frac{3}{28}$.<br \/>\n\u00ad<\/li>\n<li>Logo, $P(\\text{&#8221;praticar futebol mas n }\\!\\!\\tilde{\\mathrm{a}}\\!\\!\\text{ o basquetebol&#8221;})=\\frac{12}{28}=\\frac{3}{7}$.<br \/>\n\u00ad<\/li>\n<li>Logo, $P(\\text{&#8221;praticar basquetebol mas n }\\!\\!\\tilde{\\mathrm{a}}\\!\\!\\text{ o futebol&#8221;})=\\frac{13}{28}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6942' onClick='GTTabs_show(0,6942)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Foi feito um inqu\u00e9rito aos 28 alunos da turma da Maria Jos\u00e9 sobre os desportos que praticavam. Concluiu-se que 15 praticavam futebol e 16 basquetebol. (Qualquer aluno da turma pratica pelo&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20341,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,217,215],"series":[],"class_list":["post-6942","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-estatistica-e-probabilidades","tag-9-o-ano","tag-acontecimento","tag-probabilidade"],"views":2320,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9V1Pag023-18_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6942","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=6942"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6942\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20341"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6942"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6942"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}