{"id":7038,"date":"2011-10-13T22:03:20","date_gmt":"2011-10-13T21:03:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7038"},"modified":"2022-01-25T16:29:36","modified_gmt":"2022-01-25T16:29:36","slug":"um-dado-esta-viciado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7038","title":{"rendered":"Um dado est\u00e1 viciado"},"content":{"rendered":"<p><ul id='GTTabs_ul_7038' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7038' class='GTTabs_curr'><a  id=\"7038_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7038' ><a  id=\"7038_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_7038'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/dado.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7039\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7039\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/dado.jpg\" data-orig-size=\"193,204\" 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=\"Dado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/dado.jpg\" class=\"alignright size-full wp-image-7039\" title=\"Dado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/dado.jpg\" alt=\"\" width=\"135\" height=\"143\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/dado.jpg 193w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/dado-141x150.jpg 141w\" sizes=\"auto, (max-width: 135px) 100vw, 135px\" \/><\/a>Um dado est\u00e1 viciado de tal modo que a probabilidade de obter um n\u00famero par \u00e9 dupla da probabilidade de obter um n\u00famero \u00edmpar.<\/p>\n<ol>\n<li>Qual a probabilidade de obter um n\u00famero par?<\/li>\n<li>Qual a probabilidade de obter 1 ponto.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7038' onClick='GTTabs_show(1,7038)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7038'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Os acontecimentos elementares verificam as seguintes condi\u00e7\u00f5es:<br \/>\n$P(&#8221;1&#8221;)=P(&#8221;3&#8221;)=P(&#8221;5&#8221;)=p$ e $P(&#8221;2&#8221;)=P(&#8221;4&#8221;)=P(&#8221;6&#8221;)=2p$.<\/p>\n<p>Como os acontecimentos elementares s\u00e3o disjuntos dois a dois, a sua uni\u00e3o \u00e9 o espa\u00e7o de resultados S.<\/p>\n<p>Logo, $P(S)=1\\Leftrightarrow P(&#8221;1&#8221;)+P(&#8221;3&#8221;)+P(&#8221;5&#8221;)+P(&#8221;2&#8221;)+P(&#8221;4&#8221;)+P(&#8221;6&#8221;)=1$, donde $3\\times p+3\\times 2p=1\\Leftrightarrow p=\\frac{1}{9}$.<\/p>\n<p>Portanto, a probabilidade de obter um n\u00famero par \u00e9 $\\frac{2}{9}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>A probabilidade de obter 1 ponto \u00e9 $P(&#8221;1&#8221;)=\\frac{1}{9}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7038' onClick='GTTabs_show(0,7038)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um dado est\u00e1 viciado de tal modo que a probabilidade de obter um n\u00famero par \u00e9 dupla da probabilidade de obter um n\u00famero \u00edmpar. Qual a probabilidade de obter um n\u00famero&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20985,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,227],"tags":[427,217,216,215],"series":[],"class_list":["post-7038","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-12--ano","category-probabilidades-e-combinatoria","tag-12-o-ano","tag-acontecimento","tag-espaco-de-resultados","tag-probabilidade"],"views":2680,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag168-20_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7038","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=7038"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7038\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20985"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7038"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7038"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7038"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7038"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}