{"id":7087,"date":"2011-10-17T00:57:01","date_gmt":"2011-10-16T23:57:01","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7087"},"modified":"2021-12-28T21:43:58","modified_gmt":"2021-12-28T21:43:58","slug":"prove-que-4","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7087","title":{"rendered":"Prove que"},"content":{"rendered":"<p><ul id='GTTabs_ul_7087' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7087' class='GTTabs_curr'><a  id=\"7087_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7087' ><a  id=\"7087_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_7087'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Seja S o espa\u00e7o de resultados associado a uma certa experi\u00eancia aleat\u00f3ria.<\/p>\n<p>Sejam A e B dois acontecimentos poss\u00edveis ($A\\subset S$ e $B\\subset S$).<\/p>\n<p>Sabe-se que:<\/p>\n<ul>\n<li>$P(A\\cap B)=0,1$<\/li>\n<li>$P(A\\cup B)=0,8$<\/li>\n<li>$P(A|B)=0,25$<\/li>\n<\/ul>\n<p>Prove que $A$ e $\\overline{A}$ s\u00e3o acontecimentos equiprov\u00e1veis.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7087' onClick='GTTabs_show(1,7087)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7087'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Como \u00e9 sabido, $P(A|B)=\\frac{P(A\\cap B)}{P(B)}$.<br \/>\nDonde, substituindo os valores conhecidos, temos: \\[\\begin{array}{*{35}{l}}<br \/>\n0,25=\\frac{0,1}{P(B)} &amp; \\Leftrightarrow\u00a0 &amp; P(B)=\\frac{0,1}{0,25}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; P(B)=0,4\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Por outro lado, sabemos que $P(A\\cup B)=P(A)+P(B)-P(A\\cap B)$.<br \/>\nLogo, tem-se: \\[\\begin{array}{*{35}{l}}<br \/>\n0,8=P(A)+0,4-0,1 &amp; \\Leftrightarrow\u00a0 &amp; P(A)=0,5\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Como $P(\\overline{A})=1-P(A)=1-0,5=0,5=P(A)$, ent\u00e3o os acontecimentos $A$ e $\\overline{A}$ s\u00e3o equiprov\u00e1veis<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7087' onClick='GTTabs_show(0,7087)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seja S o espa\u00e7o de resultados associado a uma certa experi\u00eancia aleat\u00f3ria. Sejam A e B dois acontecimentos poss\u00edveis ($A\\subset S$ e $B\\subset S$). Sabe-se que: $P(A\\cap B)=0,1$ $P(A\\cup B)=0,8$ $P(A|B)=0,25$&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19505,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,215,235],"series":[],"class_list":["post-7087","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-probabilidade","tag-probabilidade-condicionada"],"views":1968,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat137.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7087","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=7087"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7087\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19505"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7087"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7087"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7087"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7087"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}