{"id":6958,"date":"2011-10-03T16:08:38","date_gmt":"2011-10-03T15:08:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6958"},"modified":"2022-01-16T03:19:07","modified_gmt":"2022-01-16T03:19:07","slug":"lancou-se-uma-moeda-ao-ar-quatro-vezes","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6958","title":{"rendered":"Lan\u00e7ou-se uma moeda ao ar quatro vezes"},"content":{"rendered":"<p><ul id='GTTabs_ul_6958' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6958' class='GTTabs_curr'><a  id=\"6958_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6958' ><a  id=\"6958_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_6958'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1euro-b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6960\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6960\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1euro-b.png\" data-orig-size=\"96,90\" 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=\"1 \u20ac\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1euro-b.png\" class=\"alignright wp-image-6960 size-full\" title=\"1 \u20ac\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/1euro-b.png\" alt=\"\" width=\"96\" height=\"90\" \/><\/a>Lan\u00e7ou-se uma moeda ao ar quatro vezes.<\/p>\n<p>Qual a probabilidade de:<\/p>\n<ol>\n<li>sair quatro vezes a face portuguesa?<\/li>\n<li>sair duas vezes e s\u00f3 duas vezes a face comum a todos os pa\u00edses da Uni\u00e3o Europeia?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6958' onClick='GTTabs_show(1,6958)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6958'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Consideremos os acontecimentos P: &#8220;sair face portuguesa&#8221; e C: &#8220;sair face comum&#8221;, no lan\u00e7amento da moeda (uma vez).<\/p>\n<p>Relativamente \u00e0 experi\u00eancia aleat\u00f3ria descrita, h\u00e1 16 casos poss\u00edveis: $NCP=2\\times 2\\times 2\\times 2=16$. (Porqu\u00ea?)<\/p>\n<p>Esses resultados podem ser expressos da seguinte maneira:<\/p>\n<ul>\n<li>PPPP &#8211; Nos quatro lan\u00e7amentos da moeda, saiu sempre face portuguesa;<\/li>\n<li>CCPC &#8211; Apenas saiu face portuguesa no 3.\u00ba lan\u00e7amento;<\/li>\n<li>&#8230;<\/li>\n<\/ul>\n<ol>\n<li>Seja X: &#8220;sair quatro vezes a face portuguesa&#8221;.<br \/>\nApenas h\u00e1 um caso favor\u00e1vel a este acontecimento: PPPP.<br \/>\nLogo, $P(X)=\\frac{1}{16}$.<br \/>\n\u00ad<\/li>\n<li>Seja Y: &#8220;sair duas vezes e s\u00f3 duas vezes a face comum a todos os pa\u00edses da Uni\u00e3o Europeia&#8221;.<br \/>\nH\u00e1 6 casos favor\u00e1veis a este acontecimento: CCPP, CPCP, CPPC, PCCP, PCPC e\u00a0PPCC. (Porqu\u00ea?)<br \/>\nLogo, $P(Y)=\\frac{6}{16}=\\frac{3}{8}$.<\/li>\n<\/ol>\n<p>O racioc\u00ednio utilizado pode se esclarecido pelo diagrama seguinte:<\/p>\n<p style=\"text-align: center;\">\u00a0<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6961\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6961\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas.jpg\" data-orig-size=\"511,514\" 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\/4moedas.jpg\" class=\"aligncenter wp-image-6961 size-full\" title=\"Diagrama\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas.jpg\" alt=\"\" width=\"511\" height=\"514\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas.jpg 511w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas-150x150.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas-298x300.jpg 298w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4moedas-400x402.jpg 400w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/a><\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6958' onClick='GTTabs_show(0,6958)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Lan\u00e7ou-se uma moeda ao ar quatro vezes. Qual a probabilidade de: sair quatro vezes a face portuguesa? sair duas vezes e s\u00f3 duas vezes a face comum a todos os pa\u00edses&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20347,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,217,218,215],"series":[],"class_list":["post-6958","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-espaco-de-acontecimentos","tag-probabilidade"],"views":3503,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/9CA-Pag004-13-b_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6958","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=6958"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6958\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20347"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6958"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}