{"id":7040,"date":"2011-10-13T22:46:57","date_gmt":"2011-10-13T21:46:57","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7040"},"modified":"2021-12-28T23:18:05","modified_gmt":"2021-12-28T23:18:05","slug":"prove-que-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7040","title":{"rendered":"Prove que"},"content":{"rendered":"<p><ul id='GTTabs_ul_7040' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7040' class='GTTabs_curr'><a  id=\"7040_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7040' ><a  id=\"7040_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_7040'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Prove que, sendo $A\\cap B=\\left\\{ {} \\right\\}$, ent\u00e3o:<\/p>\n<ol>\n<li>$P(A)+P(B)+P(\\overline{A\\cup B})=1$<\/li>\n<li>$P(\\overline{A\\cup B})=P(\\overline{A})-P(B)$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7040' onClick='GTTabs_show(1,7040)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7040'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>\u00a0$P(A)+P(B)+P(\\overline{A\\cup B})=1$, com $A\\cap B=\\left\\{ {} \\right\\}$.\n<p>Ora, \\[\\begin{array}{*{35}{l}}<br \/>\nP(A)+P(B)+P(\\overline{A\\cup B}) &amp; = &amp; P(A)+P(B)+1-P(A\\cup B)\u00a0 \\\\<br \/>\n{} &amp; = &amp; P(A)+P(B)+1-P(A)-P(B)+P(A\\cap B)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1+P(A\\cap B)\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nComo $A\\cap B=\\left\\{ {} \\right\\}$, ent\u00e3o $P(A\\cap B)=0$.<\/p>\n<p>Logo, sendo $A\\cap B=\\left\\{ {} \\right\\}$, ent\u00e3o $P(A)+P(B)+P(\\overline{A\\cup B})=1$.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>$P(\\overline{A\\cup B})=P(\\overline{A})-P(B)$, com $A\\cap B=\\left\\{ {} \\right\\}$.\n<p>Ora, \\[\\begin{array}{*{35}{l}}<br \/>\nP(\\overline{A\\cup B}) &amp; = &amp; 1-P(A\\cup B)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 1-P(A)-P(B)+P(A\\cap B)\u00a0 \\\\<br \/>\n{} &amp; = &amp; P(\\overline{A})-P(B)+P(A\\cap B)\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nComo $A\\cap B=\\left\\{ {} \\right\\}$, ent\u00e3o $P(A\\cap B)=0$.<\/p>\n<p>Logo, sendo $A\\cap B=\\left\\{ {} \\right\\}$, ent\u00e3o $P(\\overline{A\\cup B})=P(\\overline{A})-P(B)$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7040' onClick='GTTabs_show(0,7040)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Prove que, sendo $A\\cap B=\\left\\{ {} \\right\\}$, ent\u00e3o: $P(A)+P(B)+P(\\overline{A\\cup B})=1$ $P(\\overline{A\\cup B})=P(\\overline{A})-P(B)$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19179,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,234,215],"series":[],"class_list":["post-7040","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-axiomatica","tag-probabilidade"],"views":1739,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat70.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7040","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=7040"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7040\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19179"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7040"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7040"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7040"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7040"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}