{"id":7033,"date":"2011-10-13T02:04:51","date_gmt":"2011-10-13T01:04:51","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7033"},"modified":"2026-06-05T00:22:16","modified_gmt":"2026-06-04T23:22:16","slug":"o-jogo-solitario-da-roleta-russa","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7033","title":{"rendered":"O jogo solit\u00e1rio da roleta russa"},"content":{"rendered":"<p><ul id='GTTabs_ul_7033' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7033' class='GTTabs_curr'><a  id=\"7033_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7033' ><a  id=\"7033_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_7033'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<div id=\"attachment_7034\" style=\"width: 176px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Graham_Greene.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7034\" data-attachment-id=\"7034\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7034\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Graham_Greene.jpg\" data-orig-size=\"207,264\" 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=\"Graham Greene\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Henry Graham Greene (2-10-1904 &amp;#8211; 3-04-1991)&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Graham_Greene.jpg\" class=\"size-full wp-image-7034  \" title=\"Graham Greene\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Graham_Greene.jpg\" alt=\"\" width=\"166\" height=\"211\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Graham_Greene.jpg 207w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Graham_Greene-117x150.jpg 117w\" sizes=\"auto, (max-width: 166px) 100vw, 166px\" \/><\/a><p id=\"caption-attachment-7034\" class=\"wp-caption-text\">Henry Graham Greene<\/p><\/div>\n<p>&#8220;&#8230; perguntei a <a href=\"https:\/\/en.wikipedia.org\/wiki\/Graham_Greene\" target=\"_blank\" rel=\"noopener\">Graham Greene<\/a> o que havia de verdade no epis\u00f3dio da roleta russa que ele relatara nas suas mem\u00f3rias. Os seus olhos azuis, os mais di\u00e1fanos que conheci, iluminaram-se com a recorda\u00e7\u00e3o. &#8220;<em>Isso foi aos dezanove anos<\/em>&#8220;, disse, &#8220;<em>quando me apaixonei pela professora da minha irm\u00e3<\/em>&#8220;. Contou que, de facto, tinha ent\u00e3o jogado o jogo solit\u00e1rio da roleta russa, com um velho rev\u00f3lver de um irm\u00e3o, em quatro ocasi\u00f5es diferentes. Entre as duas primeiras houve uma semana de intervalo, mas as duas \u00faltimas foram seguidas e com poucos minutos de diferen\u00e7a.<\/p>\n<div id=\"attachment_7035\" style=\"width: 157px\" class=\"wp-caption alignright\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7035\" data-attachment-id=\"7035\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7035\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro.jpg\" data-orig-size=\"436,458\" 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=\"Fidel Castro\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Fidel Alejandro Castro Ruz&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro.jpg\" class=\"size-full wp-image-7035 \" title=\"Fidel Castro\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro.jpg\" alt=\"\" width=\"147\" height=\"154\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro.jpg 436w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro-285x300.jpg 285w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro-142x150.jpg 142w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Fidel_Castro-400x420.jpg 400w\" sizes=\"auto, (max-width: 147px) 100vw, 147px\" \/><\/a><p id=\"caption-attachment-7035\" class=\"wp-caption-text\">Fidel Alejandro Castro Ruz<\/p><\/div>\n<p><a href=\"https:\/\/pt.wikipedia.org\/wiki\/Fidel_Castro\" target=\"_blank\" rel=\"noopener\">Fidel Castro<\/a>, que n\u00e3o podia deixar passar um relato como este sem ir at\u00e9 aos mais \u00ednfimos pormenores, perguntou-lhe para quantos proj\u00e9teis era o tambor do rev\u00f3lver. &#8220;<em>Para seis<\/em>&#8220;, respondeu Graham Greene. Ent\u00e3o Fidel fechou os olhos e come\u00e7ou a murmurar multiplica\u00e7\u00f5es. Por fim, olhou o escritor e disse-lhe: &#8220;<em>De acordo com o c\u00e1lculo das probabilidades voc\u00ea teria de estar morto<\/em>&#8220;. Graham Greene sorriu com a placidez com que o fazem os escritores que se sentem a viver um epis\u00f3dio dos seus pr\u00f3prios livros e disse: &#8220;<em>Ainda bem que sempre fui p\u00e9ssimo a Matem\u00e1tica<\/em>&#8220;&#8230;&#8221;<\/p>\n<p style=\"text-align: right;\"><span style=\"font-size: x-small;\">[Excerto do artigo &#8220;<a href=\"https:\/\/www.elpais.com\/articulo\/opinion\/CASTRO\/_FIDEL\/GREENE\/_GRAHAM\/TORRIJOS\/_OMAR_\/PANAMA\/PANAMA\/ESTADOS_UNIDOS\/CUBA\/elpepiopi\/19830119elpepiopi_13\/Tes\" target=\"_blank\" rel=\"noopener\">As Vinte Horas de Graham Greene em Havana<\/a>&#8220;, de <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Gabriel_Garc%C3%ADa_M%C3%A1rquez\" target=\"_blank\" rel=\"noopener\">Gabriel Garcia M\u00e1rquez<\/a>, publicado em 19 de Mar\u00e7o de 1983 no jornal espanhol &#8220;<em>El Pa\u00eds<\/em>&#8220;]<\/span><\/p>\n<blockquote>\n<div id=\"attachment_7036\" style=\"width: 202px\" class=\"wp-caption alignleft\"><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Gabriel_Garcia_Marquez.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-7036\" data-attachment-id=\"7036\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7036\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Gabriel_Garcia_Marquez.jpg\" data-orig-size=\"240,219\" 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=\"Gabriel Garc\u00eda M\u00e1rquez\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Gabriel Garc\u00eda M\u00e1rquez&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Gabriel_Garcia_Marquez.jpg\" class=\"size-full wp-image-7036 \" title=\"Gabriel Garc\u00eda M\u00e1rquez\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Gabriel_Garcia_Marquez.jpg\" alt=\"\" width=\"192\" height=\"175\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Gabriel_Garcia_Marquez.jpg 240w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/Gabriel_Garcia_Marquez-150x136.jpg 150w\" sizes=\"auto, (max-width: 192px) 100vw, 192px\" \/><\/a><p id=\"caption-attachment-7036\" class=\"wp-caption-text\">Gabriel Garc\u00eda M\u00e1rquez<\/p><\/div>\n<p>Por eso le pregunt\u00e9 a Graham Greene qu\u00e9 hab\u00eda de cierto en el episodio de la\u00a0<em>ruleta rusa<\/em>\u00a0que \u00e9l ha contado en sus memorias. Sus\u00a0<em>ojos<\/em>\u00a0azules, los m\u00e1s di\u00e1fanos que conozco, se iluminaron con los recuerdos. &#8220;Eso fue a los diecinueve a\u00f1os&#8221;, dijo, &#8220;cuando me enamor\u00e9 de la institutriz de mi hermana&#8221;. Cont\u00f3 que, en efecto, hab\u00eda jugado entonces al juego solitario de la\u00a0<em>ruleta rusa<\/em>\u00a0con un viejo rev\u00f3lver de un hermano mayor, y en cuatro ocasiones diferentes. Entre las dos primeras hubo una semana de intervalo, pero las dos \u00faltimas fueron sucesivas y con pocos minutos de diferencia. Fidel Castro, que no pod\u00eda pasar por alto un dato como \u00e9se sin agotar hasta las \u00faltimas precisiones, le pregunt\u00f3 para cu\u00e1ntos proyectiles era el tambor del rev\u00f3lver. &#8220;Para seis&#8221;, le contest\u00f3 Graham. Greene. Entonces, Fidel Castro cerr\u00f3 los\u00a0<em>ojos<\/em>\u00a0y empez\u00f3 a murmurar cifras de multiplicaci\u00f3n. Por \u00faltimo, mir\u00f3 al escritor con una expresi\u00f3n de asombro y le dijo: &#8220;De acuerdo con el c\u00e1lculo de las probabilidades, usted tendr\u00eda que estar muerto&#8221;. Graham Greene sonri\u00f3 con la placidez con que lo hacen todos los escritores cuando se sienten viviendo un episodio de sus propios libros, y dijo: &#8220;Menos mal que siempre fui p\u00e9simo en matem\u00e1ticas&#8221;.<\/p>\n<p style=\"text-align: right;\"><span style=\"font-size: x-small;\"><a href=\"https:\/\/www.elpais.com\/articulo\/opinion\/CASTRO\/_FIDEL\/GREENE\/_GRAHAM\/TORRIJOS\/_OMAR_\/PANAMA\/PANAMA\/ESTADOS_UNIDOS\/CUBA\/elpepiopi\/19830119elpepiopi_13\/Tes\" target=\"_blank\" rel=\"noopener\">Excerto do original<\/a><\/span><\/p>\n<\/blockquote>\n<p>Graham Greene jogou 4 vezes a roleta russa.<br \/>\nConcorda que, segundo o c\u00e1lculo das probabilidades, ele deveria estar morto? Justifique a sua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7033' onClick='GTTabs_show(1,7033)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7033'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><strong><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7037\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7037\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa.jpg\" data-orig-size=\"400,329\" 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=\"roletarussa\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa.jpg\" class=\"alignright size-full wp-image-7037\" title=\"roletarussa\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa.jpg\" alt=\"\" width=\"144\" height=\"118\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa-300x246.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/roletarussa-150x123.jpg 150w\" sizes=\"auto, (max-width: 144px) 100vw, 144px\" \/><\/a><a href=\"https:\/\/pt.wikipedia.org\/wiki\/Roleta_russa\" target=\"_blank\" rel=\"noopener\">Roleta russa<\/a><\/strong>\u00a0\u00e9 um\u00a0jogo de azar\u00a0onde os participantes colocam uma bala \u2014 tipicamente apenas uma \u2014 em uma das c\u00e2maras de um rev\u00f3lver. O tambor do rev\u00f3lver \u00e9 girado e fechado, de modo que a localiza\u00e7\u00e3o da bala \u00e9 desconhecida. Os participantes apontam a arma para suas cabe\u00e7as e atiram, correndo o risco da prov\u00e1vel morte caso a bala esteja na c\u00e2mara engatilhada.<\/p>\n<\/blockquote>\n<p>Em cada um dos jogos h\u00e1 seis possibilidades de selecionar uma das c\u00e2mara do rev\u00f3lver, pelo que o n\u00famero de casos poss\u00edveis \u00e9 $NCP=6\\times 6\\times 6\\times 6={{6}^{4}}$.<\/p>\n<p>O n\u00famero de casos favor\u00e1veis \u00e0 c\u00e2mara que cont\u00e9m o proj\u00e9til n\u00e3o ser selecionada at\u00e9 ao 4.\u00ba jogo \u00e9 $NCF=5\\times 5\\times 5\\times 5={{5}^{4}}$.<\/p>\n<p>Assim, segundo o c\u00e1lculo das probabilidades, ele apenas deveria estar \u00abmeio morto\u00bb, pois $P(&#8221;\\text{estar vivo}&#8221;)={{\\left( \\frac{5}{6} \\right)}^{4}}\\approx 0,48$ e $P(&#8221;\\text{estar morto}&#8221;)=1-{{\\left( \\frac{5}{6} \\right)}^{4}}\\approx 0,52$.<\/p>\n<p>De qualquer forma, ainda que n\u00e3o fosse muito prov\u00e1vel ter morrido no \u00faltimo jogo, se estava vivo, teve muita sorte!<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7033' onClick='GTTabs_show(0,7033)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado &#8220;&#8230; perguntei a Graham Greene o que havia de verdade no epis\u00f3dio da roleta russa que ele relatara nas suas mem\u00f3rias. Os seus olhos azuis, os mais di\u00e1fanos que conheci, iluminaram-se&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20983,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,217,216,233,231,232,215],"series":[],"class_list":["post-7033","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-fidel-castro","tag-gabriel-garcia-marquez","tag-graham-greene","tag-probabilidade"],"views":2566,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag167-19-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\/7033","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=7033"}],"version-history":[{"count":5,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7033\/revisions"}],"predecessor-version":[{"id":27899,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7033\/revisions\/27899"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20983"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7033"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}