{"id":7242,"date":"2011-12-03T22:04:38","date_gmt":"2011-12-03T22:04:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7242"},"modified":"2022-01-25T23:52:31","modified_gmt":"2022-01-25T23:52:31","slug":"grupos-sanguineos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7242","title":{"rendered":"Grupos sangu\u00edneos"},"content":{"rendered":"<p><ul id='GTTabs_ul_7242' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7242' class='GTTabs_curr'><a  id=\"7242_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7242' ><a  id=\"7242_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_7242'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/blood-drive.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7243\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7243\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/blood-drive.jpg\" data-orig-size=\"351,565\" 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=\"Sangue\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/blood-drive.jpg\" class=\"alignright size-full wp-image-7243\" title=\"Sangue\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/blood-drive.jpg\" alt=\"\" width=\"127\" height=\"203\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/blood-drive.jpg 351w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/blood-drive-93x150.jpg 93w\" sizes=\"auto, (max-width: 127px) 100vw, 127px\" \/><\/a>Os seres humanos est\u00e3o repartidos, segundo a composi\u00e7\u00e3o do seu sangue, em quatros grupos: O, A, B e AB.<\/p>\n<p>Num conjunto de 10 dadores de sangue, quatro pertencem ao grupo O, tr\u00eas ao grupo A, dois ao grupo B e um ao grupo AB.<\/p>\n<p>Escolhidas, ao acaso, quatro pessoas desse conjunto:<\/p>\n<ol>\n<li>qual \u00e9 a probabilidade das quatro pertencerem ao mesmo grupo sangu\u00edneo?<\/li>\n<li>qual \u00e9 a probabilidade de pelo menos tr\u00eas delas pertencerem ao mesmo grupo sangu\u00edneo?<\/li>\n<li>sabendo que tr\u00eas, e s\u00f3 tr\u00eas, pertencem ao mesmo grupo sangu\u00edneo, qual \u00e9 a probabilidade desse grupo ser o grupo O?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7242' onClick='GTTabs_show(1,7242)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7242'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\" aligncenter\" style=\"width: 60%;\" border=\"0\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"background-color: #b0e0e6; border: #00008b 1px solid;\">Grupo sangu\u00edneo<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">O<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">A<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">B<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">AB<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">Total<\/td>\n<\/tr>\n<tr>\n<td style=\"background-color: #b0e0e6; border: #00008b 1px solid;\">Dadores de sangue<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">4<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">3<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">2<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">1<\/td>\n<td style=\"text-align: center; background-color: #b0e0e6; border: #00008b 1px solid;\">10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Para que os quatro dadores perten\u00e7am ao mesmo grupo sangu\u00edneo t\u00eam de ser do grupo O.<br \/>\nAssim, a probabilidade pedida \u00e9 $$p=\\frac{{}^{4}{{C}_{4}}}{{}^{10}{{C}_{4}}}=\\frac{1}{210}$$<\/li>\n<li>Como vimos, o m\u00e1ximo de dadores do mesmo grupo sangu\u00edneo \u00e9 quatro, pertencendo ao grupo O.<br \/>\nQuanto a tr\u00eas dadores do mesmo grupo, tanto podem ser do grupo O, como do grupo A.<br \/>\nAssim, a probabilidade pedida \u00e9 $$p=\\frac{\\overbrace{{}^{4}{{C}_{4}}}^{O}+\\overbrace{{}^{4}{{C}_{3}}}^{O}\\times \\overbrace{{}^{6}{{C}_{1}}}^{\\overline{O}}+\\overbrace{{}^{3}{{C}_{3}}}^{A}\\times \\overbrace{{}^{7}{{C}_{1}}}^{\\overline{A}}}{{}^{10}{{C}_{4}}}=\\frac{1+4\\times 6+1\\times 7}{210}=\\frac{32}{210}=\\frac{16}{105}$$<\/li>\n<li>Se tr\u00eas, e s\u00f3 tr\u00eas, pertencem ao mesmo grupo sangu\u00edneo, ent\u00e3o:\n<p>Caso 1: Essas tr\u00eas pessoas s\u00e3o do grupo O e a quarta \u00e9 do A, B ou AB;<\/p>\n<p>Caso 2: Essas tr\u00eas pessoas s\u00e3o do grupo A e a quarta \u00e9 do grupo O, B ou AB.<\/p>\n<p>Assim, o n\u00famero de casos poss\u00edveis \u00e9 $NCP={}^{4}{{C}_{3}}\\times {}^{6}{{C}_{1}}+{}^{3}{{C}_{3}}\\times {}^{7}{{C}_{1}}=4\\times 6+1\\times 7=31$ e o n\u00famero de casos favor\u00e1veis \u00e9 $NCF={}^{4}{{C}_{3}}\\times {}^{6}{{C}_{1}}=24$.<\/p>\n<p>Portanto, a probabilidade pedida \u00e9 $$p=\\frac{{}^{4}{{C}_{3}}\\times {}^{6}{{C}_{1}}}{{}^{4}{{C}_{3}}\\times {}^{6}{{C}_{1}}+{}^{3}{{C}_{3}}\\times {}^{7}{{C}_{1}}}=\\frac{24}{31}$$<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7242' onClick='GTTabs_show(0,7242)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Os seres humanos est\u00e3o repartidos, segundo a composi\u00e7\u00e3o do seu sangue, em quatros grupos: O, A, B e AB. Num conjunto de 10 dadores de sangue, quatro pertencem ao grupo O,&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21057,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255,215],"series":[],"class_list":["post-7242","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-probabilidade"],"views":2786,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/12\/12V1Pag179-66_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7242","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=7242"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7242\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21057"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7242"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7242"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7242"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7242"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}