{"id":7043,"date":"2011-10-14T01:23:15","date_gmt":"2011-10-14T00:23:15","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7043"},"modified":"2022-01-25T16:39:15","modified_gmt":"2022-01-25T16:39:15","slug":"estudo-de-linguas-estrangeiras","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7043","title":{"rendered":"Estudo de l\u00ednguas estrangeiras (1)"},"content":{"rendered":"<p><ul id='GTTabs_ul_7043' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7043' class='GTTabs_curr'><a  id=\"7043_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7043' ><a  id=\"7043_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_7043'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7044\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7044\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos.jpg\" data-orig-size=\"301,343\" 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=\"Alunos\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos.jpg\" class=\"alignright size-full wp-image-7044\" title=\"Alunos\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos.jpg\" alt=\"\" width=\"181\" height=\"206\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos.jpg 301w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos-263x300.jpg 263w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/alunos-131x150.jpg 131w\" sizes=\"auto, (max-width: 181px) 100vw, 181px\" \/><\/a>Numa classe, todos os alunos estudam duas, e s\u00f3 duas, l\u00ednguas estrangeiras: ou Ingl\u00eas (I) e Alem\u00e3o (A) ou Ingl\u00eas (I) e Espanhol (E).<\/p>\n<p>A reparti\u00e7\u00e3o de alunos \u00e9 a seguinte:<\/p>\n<table class=\" aligncenter\" style=\"width: 30%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #fb92a3;\">Carater\u00edstica<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">FA<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">MA<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">FE<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">ME<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #fb92a3;\">Efetivos<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">12<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">6<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">8<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Em que M representa rapaz e F rapariga.<\/p>\n<ol>\n<li>Calcule a probabilidade dos acontecimentos:\n<p>a) M: &#8220;o aluno \u00e9 um rapaz&#8221;;<\/p>\n<p>b) E: &#8220;o aluno estuda Espanhol&#8221;;<\/p>\n<p>c) $F\\cap A$: &#8220;o aluno \u00e9 uma rapariga que estuda alem\u00e3o&#8221;.<\/p>\n<\/li>\n<li>Determine a probabilidade de interrogar:\n<p>a) um estudante de Alem\u00e3o, sabendo que \u00e9 rapariga;<\/p>\n<p>b) uma rapariga, sabendo que estuda alem\u00e3o.<\/p>\n<\/li>\n<li>No corredor passamos por um rapaz da classe.<br \/>\nQual \u00e9 a probabilidade de ele estudar Espanhol?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7043' onClick='GTTabs_show(1,7043)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7043'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<table class=\" aligncenter\" style=\"width: 30%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #fb92a3;\">Carater\u00edstica<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">FA<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">MA<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">FE<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">ME<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #fb92a3;\">Efetivos<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">12<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">6<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">8<\/td>\n<td style=\"text-align: center; background-color: #eeeeee;\">10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ul>\n<li>N\u00famero de alunos: $12+6+8+10=36$<\/li>\n<li>N\u00famero de rapazes: $6+10=16$<\/li>\n<li>N\u00famero de raparigas: $12+8=20$<br \/>\n\u00ad<\/li>\n<\/ul>\n<ol>\n<li>a)<br \/>\nM: &#8220;o aluno \u00e9 um rapaz&#8221;.<\/p>\n<p>A probabilidade pedida \u00e9 $P(M)=\\frac{16}{36}=\\frac{4}{9}$.<\/p>\n<p>b)<br \/>\nE: &#8220;o aluno estuda Espanhol&#8221;.<\/p>\n<p>A probabilidade pedida \u00e9 $P(E)=\\frac{18}{36}=\\frac{1}{2}$.<\/p>\n<p>c)<br \/>\n$F\\cap A$: &#8220;o aluno \u00e9 uma rapariga que estuda alem\u00e3o&#8221;.<\/p>\n<p>A probabilidade pedida \u00e9 $P(F\\cap A)=\\frac{12}{36}=\\frac{1}{3}$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>a)<br \/>\n&#8220;um estudante de Alem\u00e3o, sabendo que \u00e9 rapariga&#8221;.<\/p>\n<p>A probabilidade pedida \u00e9 $P(A|F)=\\frac{12}{20}=\\frac{3}{5}$, pois as raparigas s\u00e3o 20, estudando Alem\u00e3o 12 delas.<br \/>\nOu, ent\u00e3o, \\[P(A|F)=\\frac{P(A\\cap F)}{P(F)}=\\frac{\\frac{12}{36}}{\\frac{20}{36}}=\\frac{3}{5}\\]<\/p>\n<p>b)<br \/>\n&#8220;uma rapariga, sabendo que estuda alem\u00e3o&#8221;.<\/p>\n<p>A probabilidade pedida \u00e9 $P(F|A)=\\frac{12}{18}=\\frac{2}{3}$, pois dos 18 alunos que estudam Alem\u00e3o, 12 deles s\u00e3o raparigas.<br \/>\nOu, ent\u00e3o, \\[P(F|A)=\\frac{P(A\\cap F)}{P(A)}=\\frac{\\frac{12}{36}}{\\frac{18}{36}}=\\frac{2}{3}\\]<br \/>\n\u00ad<\/p>\n<\/li>\n<li>No corredor passamos por um rapaz da classe.<br \/>\nQual \u00e9 a probabilidade de ele estudar Espanhol?<\/p>\n<p>A probabilidade pedida \u00e9 $P(E|M)=\\frac{10}{16}=\\frac{5}{8}$, pois 16 alunos s\u00e3o rapazes, estudando Espanhol 10 deles.<br \/>\nOu, ent\u00e3o, \\[P(E|M)=\\frac{P(E\\cap M)}{P(M)}=\\frac{\\frac{10}{36}}{\\frac{16}{36}}=\\frac{5}{8}\\]<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7043' onClick='GTTabs_show(0,7043)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Numa classe, todos os alunos estudam duas, e s\u00f3 duas, l\u00ednguas estrangeiras: ou Ingl\u00eas (I) e Alem\u00e3o (A) ou Ingl\u00eas (I) e Espanhol (E). A reparti\u00e7\u00e3o de alunos \u00e9 a seguinte:&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20987,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,217,216,215,235],"series":[],"class_list":["post-7043","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-probabilidade","tag-probabilidade-condicionada"],"views":1991,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag168-22_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7043","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=7043"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7043\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20987"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7043"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7043"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7043"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}