{"id":7078,"date":"2011-10-16T21:51:50","date_gmt":"2011-10-16T20:51:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7078"},"modified":"2022-01-25T18:03:23","modified_gmt":"2022-01-25T18:03:23","slug":"duas-caixas-com-bolas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7078","title":{"rendered":"Duas caixas com bolas"},"content":{"rendered":"<p><ul id='GTTabs_ul_7078' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7078' class='GTTabs_curr'><a  id=\"7078_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7078' ><a  id=\"7078_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_7078'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/2caixas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7082\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7082\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/2caixas.jpg\" data-orig-size=\"127,168\" 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=\"Duas caixas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/2caixas.jpg\" class=\"alignright size-full wp-image-7082\" title=\"Duas caixas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/2caixas.jpg\" alt=\"\" width=\"127\" height=\"168\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/2caixas.jpg 127w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/2caixas-113x150.jpg 113w\" sizes=\"auto, (max-width: 127px) 100vw, 127px\" \/><\/a>Considere duas caixas: caixa A e caixa B.<\/p>\n<ul>\n<li>A caixa A cont\u00e9m duas bolas verdes e cinco azuis.<\/li>\n<li>A caixa B cont\u00e9m seis bolas verdes e uma azul.<\/li>\n<\/ul>\n<p>Lan\u00e7a-se um dado equilibrado, com as faces numeradas de 1 a 6.<\/p>\n<ul>\n<li>Se sair face 1, tira-se, ao acaso, uma bola da caixa A.<\/li>\n<li>Caso contr\u00e1rio, tira-se, ao acaso, uma bola da caixa B.<\/li>\n<\/ul>\n<p>Considere os acontecimentos:<\/p>\n<ul>\n<li>X: <em>Sair face par no lan\u00e7amento do dado<\/em><\/li>\n<li>y: <em>Sair bola verde<\/em><\/li>\n<\/ul>\n<p>Sem aplicar a f\u00f3rmula da probabilidade condicionada, indique o valor de $P(Y|X)$ e, numa pequena composi\u00e7\u00e3o (cinco a dez linhas), justifique a sua resposta.<\/p>\n<p><strong>Nota<\/strong>: comece por indicar o significado de $P(Y|X)$, no contexto da situa\u00e7\u00e3o descrita.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7078' onClick='GTTabs_show(1,7078)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7078'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\"aligncenter\" style=\"width: 80%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #eeeeee;\"><strong>Caixa A<\/strong><\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\"><strong>Caixa B<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\u00a0<img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola azul\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-azul1.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola azul\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-azul1.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola azul\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-azul1.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola azul\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-azul1.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola azul\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-azul1.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola verde\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-verde.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><img loading=\"lazy\" decoding=\"async\" title=\"Bola azul\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/b-azul1.jpg\" alt=\"\" width=\"43\" height=\"43\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">\u00a0No dado sai face: 1<\/td>\n<td style=\"text-align: center;\">\u00a0No dado sai face: 2, 3, 4, 5 ou 6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>X: <em>Sair face par no lan\u00e7amento do dado<\/em><\/li>\n<li>y: <em>Sair bola verde<\/em><\/li>\n<\/ul>\n<p>$P(Y|X)$ \u00e9 a probabilidade de sair bola azul, se saiu face par no lan\u00e7amento do dado.<\/p>\n<p>Como saiu face par no lan\u00e7amento do dado, ser\u00e1 extra\u00edda uma bola da caixa B.<\/p>\n<p>A caixa B cont\u00e9m sete bolas (seis verdes e uma azul), pelo que a probabilidade de sair uma bola verde\u00a0\u00e9 $\\frac{6}{7}$.<\/p>\n<p>Logo, $P(Y|X)=\\frac{6}{7}$.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7078' onClick='GTTabs_show(0,7078)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considere duas caixas: caixa A e caixa B. A caixa A cont\u00e9m duas bolas verdes e cinco azuis. A caixa B cont\u00e9m seis bolas verdes e uma azul. Lan\u00e7a-se um dado&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21002,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,217,215,235],"series":[],"class_list":["post-7078","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-acontecimento","tag-probabilidade","tag-probabilidade-condicionada"],"views":4379,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12-DuasCaixasComBolas.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7078","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=7078"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7078\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21002"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7078"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7078"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7078"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7078"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}