{"id":7239,"date":"2011-12-03T20:49:55","date_gmt":"2011-12-03T20:49:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7239"},"modified":"2022-01-25T23:47:18","modified_gmt":"2022-01-25T23:47:18","slug":"uma-viagem-a-paris","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7239","title":{"rendered":"Uma viagem a Paris"},"content":{"rendered":"<p><ul id='GTTabs_ul_7239' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7239' class='GTTabs_curr'><a  id=\"7239_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7239' ><a  id=\"7239_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_7239'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7240\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7240\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night.jpg\" data-orig-size=\"600,450\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;8&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;Canon PowerShot G2&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;1006537187&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;21&quot;,&quot;iso&quot;:&quot;50&quot;,&quot;shutter_speed&quot;:&quot;15&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Paris\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night.jpg\" class=\"alignright size-full wp-image-7240\" title=\"Paris\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night.jpg\" alt=\"\" width=\"216\" height=\"162\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night.jpg 600w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night-300x225.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night-150x112.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/paris_night-400x300.jpg 400w\" sizes=\"auto, (max-width: 216px) 100vw, 216px\" \/><\/a>Suponha que lhe prop\u00f5em tr\u00eas estrat\u00e9gias diferentes para ganhar uma viagem a Paris:<\/p>\n<p><em>1.\u00aa estrat\u00e9gia<\/em> &#8211; no lan\u00e7amento de uma moeda quatro vezes consecutivas, obt\u00e9m 4 faces nacionais (N) seguidas;<\/p>\n<p><em>2.\u00aa estrat\u00e9gia<\/em> &#8211; no lan\u00e7amento de uma moeda cinco vezes consecutivas, obt\u00e9m a seguinte sequ\u00eancia: NENNE;<\/p>\n<p><em>3.\u00aa estrat\u00e9gia<\/em> &#8211; no lan\u00e7amento de uma moeda cinco vezes consecutivas, obt\u00e9m 3 faces nacionais (N) e 2 faces europeias (E).<\/p>\n<p>Qual das estrat\u00e9gias escolheria?<\/p>\n<p>Fa\u00e7a uma pequena composi\u00e7\u00e3o onde explicite a estrat\u00e9gia escolhida e as raz\u00f5es da sua escolha.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7239' onClick='GTTabs_show(1,7239)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7239'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><em>1.\u00aa estrat\u00e9gia<\/em>:<\/p>\n<p>\u00a0A probabilidade de obter 4 faces nacionais seguidas, no lan\u00e7amento de uma moeda quatro vezes consecutivas, \u00e9 $${{P}_{1}}=\\frac{1}{{{2}^{4}}}=\\frac{1}{16}$$<\/p>\n<p><em>2.\u00aa estrat\u00e9gia<\/em>:<\/p>\n<p>A probabilidade de obter a sequ\u00eancia NENNE, no lan\u00e7amento de uma moeda cinco vezes consecutivas, \u00e9 $${{P}_{2}}=\\frac{1}{{{2}^{5}}}=\\frac{1}{32}$$<\/p>\n<p><em>3.\u00aa estrat\u00e9gia<\/em>:<\/p>\n<p>A vari\u00e1vel aleat\u00f3ria\u00a0$X$: &#8220;<em>N\u00famero de faces nacionais sa\u00eddas nos cinco lan\u00e7amentos<\/em>&#8221; tem distribui\u00e7\u00e3o binomial de par\u00e2metros $n=5$ e $p=\\frac{1}{2}$.<\/p>\n<p>Logo, a probabilidade de obter 3 faces nacionais e 2 faces europeias, no lan\u00e7amento de uma moeda cinco vezes consecutivas, \u00e9 $${{P}_{3}}=P(X=3)={}^{5}{{C}_{3}}\\times {{\\left( \\frac{1}{2} \\right)}^{3}}\\times {{\\left( \\frac{1}{2} \\right)}^{2}}=10\\times {{\\left( \\frac{1}{2} \\right)}^{5}}=\\frac{10}{32}=\\frac{5}{16}$$<\/p>\n<p>Conclus\u00e3o:<\/p>\n<p>Como ${{P}_{3}}&gt;{{P}_{1}}&gt;{{P}_{2}}$, \u00e9 de optar pela 3.\u00aa estrat\u00e9gia.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7239' onClick='GTTabs_show(0,7239)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Suponha que lhe prop\u00f5em tr\u00eas estrat\u00e9gias diferentes para ganhar uma viagem a Paris: 1.\u00aa estrat\u00e9gia &#8211; no lan\u00e7amento de uma moeda quatro vezes consecutivas, obt\u00e9m 4 faces nacionais (N) seguidas; 2.\u00aa&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21056,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255,251,215],"series":[],"class_list":["post-7239","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","tag-distribuicao-binomial","tag-probabilidade"],"views":2452,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/12V1Pag178-65_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7239","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=7239"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7239\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21056"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7239"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7239"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7239"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7239"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}