{"id":6962,"date":"2011-10-03T17:36:40","date_gmt":"2011-10-03T16:36:40","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6962"},"modified":"2022-01-16T03:26:08","modified_gmt":"2022-01-16T03:26:08","slug":"num-jantar-ha-quinze-jovens","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6962","title":{"rendered":"Num jantar h\u00e1 quinze jovens"},"content":{"rendered":"<p><ul id='GTTabs_ul_6962' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6962' class='GTTabs_curr'><a  id=\"6962_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6962' ><a  id=\"6962_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_6962'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Num jantar h\u00e1 15\u00a0jovens que falam diferentes l\u00ednguas: 8 falam ingl\u00eas, 6 falam franc\u00eas e 3 n\u00e3o falam ingl\u00eas nem franc\u00eas.<\/p>\n<ol>\n<li>Quantos jovens falam ingl\u00eas e franc\u00eas simultaneamente?<\/li>\n<li>Determina a probabilidade de, escolhendo um jovem ao acaso, encontrar um que s\u00f3 fale franc\u00eas.<\/li>\n<li>Determina a probabilidade de, escolhendo um jovem ao acaso, encontrar um que fale ingl\u00eas.<\/li>\n<li>Determina a probabilidade de, escolhendo um jovem ao acaso, encontrar um que n\u00e3o saiba falar nem franc\u00eas nem ingl\u00eas.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6962' onClick='GTTabs_show(1,6962)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6962'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Sejam J, F e I, respetivamente, o conjunto dos jovens, o conjunto dos que falam franc\u00eas e o conjunto dos que falam ingl\u00eas.<\/p>\n<p>$\\overline{F}$, conjunto complementar de F, \u00e9 o conjunto dos alunos que n\u00e3o falam franc\u00eas e, analogamente, $\\overline{I}$ \u00e9 o conjunto dos alunos que n\u00e3o falam ingl\u00eas.<\/p>\n<ol>\n<li>\u00a0<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6963\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6963\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi.jpg\" data-orig-size=\"405,255\" 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\/diagrama-fi.jpg\" class=\"alignright wp-image-6963\" title=\"Diagrama\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi.jpg\" alt=\"\" width=\"320\" height=\"201\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi.jpg 405w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi-300x188.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi-150x94.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/diagrama-fi-400x251.jpg 400w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a>De acordo com os dados, temos:\n<p>&#8211; $\\#J=15$;<\/p>\n<p>&#8211; $\\#F=6$;<\/p>\n<p>&#8211; $\\#I=8$;<\/p>\n<p>&#8211; $\\#(\\overline{F}\\cap \\overline{I})=3$.<\/p>\n<p>Como $\\#F+\\#I+\\#(\\overline{F}\\cap \\overline{I})=6+8+3=17$ e $\\#J=15$, conclui-se que $\\#(F\\cap I)=17-15=2$.<\/p>\n<p>Isto \u00e9, dois jovens falam ingl\u00eas e franc\u00eas simultaneamente.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>H\u00e1 4 jovens que s\u00f3 falam franc\u00eas.<br \/>\nLogo, a probabilidade pedida \u00e9 $p=\\frac{4}{15}$.<br \/>\n\u00ad<\/li>\n<li>H\u00e1 8 jovens que falam ingl\u00eas.<br \/>\nLogo, a probabilidade pedida \u00e9 $p=\\frac{8}{15}$.<br \/>\n\u00ad<\/li>\n<li>H\u00e1 3 jovens que n\u00e3o falam qualquer das l\u00ednguas.<br \/>\nLogo, a probabilidade pedida \u00e9 $p=\\frac{3}{15}=\\frac{1}{5}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6962' onClick='GTTabs_show(0,6962)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num jantar h\u00e1 15\u00a0jovens que falam diferentes l\u00ednguas: 8 falam ingl\u00eas, 6 falam franc\u00eas e 3 n\u00e3o falam ingl\u00eas nem franc\u00eas. Quantos jovens falam ingl\u00eas e franc\u00eas simultaneamente? Determina a probabilidade&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20348,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,217,221,218,215],"series":[],"class_list":["post-6962","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-conjunto","tag-espaco-de-acontecimentos","tag-probabilidade"],"views":1931,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/9CA-Pag005-16_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6962","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=6962"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6962\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20348"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6962"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6962"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6962"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6962"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}