{"id":6996,"date":"2011-10-10T01:01:19","date_gmt":"2011-10-10T00:01:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6996"},"modified":"2022-01-25T13:36:29","modified_gmt":"2022-01-25T13:36:29","slug":"uma-familia-com-tres-filhos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6996","title":{"rendered":"Uma fam\u00edlia com tr\u00eas filhos"},"content":{"rendered":"<p><ul id='GTTabs_ul_6996' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6996' class='GTTabs_curr'><a  id=\"6996_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6996' ><a  id=\"6996_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_6996'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/familia3filhosb.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6998\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6998\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/familia3filhosb.jpg\" data-orig-size=\"272,152\" 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=\"Tr\u00eas filhos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/familia3filhosb.jpg\" class=\"alignright wp-image-6998 size-full\" title=\"Tr\u00eas filhos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/familia3filhosb.jpg\" alt=\"\" width=\"272\" height=\"152\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/familia3filhosb.jpg 272w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/familia3filhosb-150x83.jpg 150w\" sizes=\"auto, (max-width: 272px) 100vw, 272px\" \/><\/a>Seja a experi\u00eancia aleat\u00f3ria que consiste em escolher ao acaso uma fam\u00edlia com tr\u00eas filhos e tomar nota do sexo dos filhos.<br \/>\n(Suponha que h\u00e1 equiprobabilidade em nascer rapaz ou rapariga.)<\/p>\n<ol>\n<li>Defina o espa\u00e7o de resultados S.<\/li>\n<li>Qual \u00e9 a probabilidade do acontecimento A: &#8220;o mais velho \u00e9 rapaz e seguem-se duas raparigas&#8221;?<\/li>\n<li>Qual \u00e9 a probabilidade de B: &#8220;serem todas raparigas&#8221;?<\/li>\n<li>Qual \u00e9 a probabilidade do acontecimento C: &#8220;h\u00e1 pelo menos um rapaz&#8221;?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6996' onClick='GTTabs_show(1,6996)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6996'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>O espa\u00e7o de resultados \u00e9 o conjunto $S=\\left\\{ \\text{(M}\\text{,M}\\text{,M)}\\text{, (F}\\text{,M}\\text{,M)}\\text{, (M}\\text{,F}\\text{,M)}\\text{, (M}\\text{,M}\\text{,F)}\\text{, (M}\\text{,F}\\text{,F)}\\text{, (F}\\text{,M}\\text{,F)}\\text{, (F}\\text{,F}\\text{,M)}\\text{, (F}\\text{,F}\\text{,F)} \\right\\}$.\n<p><strong>Nota<\/strong>: M &#8211; rapaz e F &#8211; rapariga.<\/p>\n<p>Os resultados poss\u00edveis podem ser obtidos com facilidade recorrendo a uma diagrama de \u00e1rvore.<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6997\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6997\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos.jpg\" data-orig-size=\"445,257\" 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\/10\/3filhos.jpg\" class=\"aligncenter size-full wp-image-6997\" title=\"Diagrama\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos.jpg\" alt=\"\" width=\"445\" height=\"257\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos.jpg 445w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos-300x173.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos-150x86.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/3filhos-400x231.jpg 400w\" sizes=\"auto, (max-width: 445px) 100vw, 445px\" \/>\u00ad<\/a><\/p>\n<\/li>\n<li>H\u00e1 apenas um resultado favor\u00e1vel ao acontecimento A: &#8220;o mais velho \u00e9 rapaz e seguem-se duas raparigas&#8221;: (M,F,F).<br \/>\nLogo, $P(A)=\\frac{1}{8}$.<br \/>\n\u00ad<\/li>\n<li>Tamb\u00e9m existe apenas um resultado favor\u00e1vel ao acontecimento B: &#8220;serem todas raparigas&#8221;: (F,F,F).<br \/>\nLogo, $P(B)=\\frac{1}{8}$.<br \/>\n\u00ad<\/li>\n<li>Relativamente ao acontecimento C: &#8220;h\u00e1 pelo menos um rapaz&#8221;, s\u00e3o favor\u00e1veis todos os resultados poss\u00edveis, com exce\u00e7\u00e3o de (F,F,F). Assim, $NCF=8-1=7$.<br \/>\nLogo, $P(C)=\\frac{7}{8}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6996' onClick='GTTabs_show(0,6996)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seja a experi\u00eancia aleat\u00f3ria que consiste em escolher ao acaso uma fam\u00edlia com tr\u00eas filhos e tomar nota do sexo dos filhos. (Suponha que h\u00e1 equiprobabilidade em nascer rapaz ou rapariga.)&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20963,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,217,216,215],"series":[],"class_list":["post-6996","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-espaco-de-resultados","tag-probabilidade"],"views":3034,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag165-8_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6996","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=6996"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6996\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20963"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6996"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}