{"id":6965,"date":"2011-10-03T23:20:09","date_gmt":"2011-10-03T22:20:09","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6965"},"modified":"2022-01-16T03:31:16","modified_gmt":"2022-01-16T03:31:16","slug":"num-saco-a-10-fichas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6965","title":{"rendered":"Num saco h\u00e1 10 fichas"},"content":{"rendered":"<p><ul id='GTTabs_ul_6965' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6965' class='GTTabs_curr'><a  id=\"6965_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6965' ><a  id=\"6965_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_6965'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Num saco h\u00e1 10 fichas indistingu\u00edveis ao tato.<\/p>\n<p>Algumas s\u00e3o vermelhas, outras s\u00e3o pretas, n\u00e3o se sabendo quantas s\u00e3o de cada cor.<\/p>\n<p>Tirou-se uma ficha, anotou-se a cor e voltou-se a coloc\u00e1-la no saco.<\/p>\n<p>Ap\u00f3s 80 extra\u00e7\u00f5es, sa\u00edram 64 vezes fichas vermelhas e 16 vezes fichas pretas.<\/p>\n<ol>\n<li>Qual a probabilidade de tirar, ao acaso, uma ficha do saco e ela ser preta?<\/li>\n<li>Qual pensas ser a composi\u00e7\u00e3o do saco? H\u00e1 mais do que uma hip\u00f3tese?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6965' onClick='GTTabs_show(1,6965)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6965'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><\/p>\n<p>Comecemos por elaborar uma tabela de frequ\u00eancias relativas simples:<\/p>\n<table class=\"aligncenter\" style=\"width: 50%;\" border=\"1\" align=\"center\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong>Cor da ficha extra\u00edda<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Freq. absoluta<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Frequ\u00eancia relativa<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Vermelha<\/td>\n<td style=\"text-align: center;\">64<\/td>\n<td style=\"text-align: center;\">0,8<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\">Preta<\/td>\n<td style=\"text-align: center;\">16<\/td>\n<td style=\"text-align: center;\">0,2<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>TOTAL<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>80<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>1<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<ol>\n<li>Admitindo que as frequ\u00eancias relativas obtidas s\u00e3o representativas das probabilidades dos respetivos acontecimentos, ser\u00e1 $P(\\text{&#8221;retirar uma ficha preta&#8221;})=0,2=\\frac{1}{5}$.<\/li>\n<li>Admita-se a suposi\u00e7\u00e3o da al\u00ednea anterior e sejam v e p, respetivamente, o n\u00famero de fichas vermelhas e o n\u00famero de fichas pretas.<br \/>\nAssim, ter-se-\u00e1:<\/p>\n<p>&#8211;\u00a0$NCP=v+p=10$;<\/p>\n<p>&#8211;\u00a0$P(\\text{&#8221;retirar uma ficha preta&#8221;})=0,2=\\frac{1}{5}$;<\/p>\n<p>&#8211;\u00a0$NCF=p$.<\/p>\n<p>Assim, temos: \\[\\begin{array}{*{35}{l}}<br \/>\nP(\\text{&#8221;retirar uma ficha preta&#8221;})=\\frac{1}{5} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{p}{10}=\\frac{1}{5}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; p=\\frac{10\\times 1}{5}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; p=2\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nPortanto, o saco cont\u00e9m 2 fichas pretas e 8 vermelhas.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6965' onClick='GTTabs_show(0,6965)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Num saco h\u00e1 10 fichas indistingu\u00edveis ao tato. Algumas s\u00e3o vermelhas, outras s\u00e3o pretas, n\u00e3o se sabendo quantas s\u00e3o de cada cor. Tirou-se uma ficha, anotou-se a cor e voltou-se a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20349,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,217,222,215],"series":[],"class_list":["post-6965","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-frequencia-relativa","tag-probabilidade"],"views":3038,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/9CA-Pag005-1_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6965","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=6965"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6965\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20349"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6965"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6965"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6965"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6965"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}