{"id":7073,"date":"2011-10-16T18:48:38","date_gmt":"2011-10-16T17:48:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7073"},"modified":"2021-12-28T22:05:34","modified_gmt":"2021-12-28T22:05:34","slug":"mostre-que-e-falsa-a-afirmacao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7073","title":{"rendered":"Mostre que \u00e9 falsa a afirma\u00e7\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_7073' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7073' class='GTTabs_curr'><a  id=\"7073_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7073' ><a  id=\"7073_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_7073'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Seja S um espa\u00e7o de resultados, finito, associado a uma experi\u00eancia aleat\u00f3ria.<\/p>\n<p>Mostre que \u00e9 falsa a seguinte afirma\u00e7\u00e3o:<\/p>\n<p>\u00abQuaisquer que sejam os acontecimentos A e B, ($A\\subset S$ e $B\\subset S$), se $P(A)+P(B)=1$, ent\u00e3o $A\\cup B$ \u00e9 um acontecimento certo.\u00bb<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7073' onClick='GTTabs_show(1,7073)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7073'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Sabe-se que $P(A\\cup B)=P(A)+P(B)-P(A\\cap B)$.<\/p>\n<p>Portanto, se $P(A)+P(B)=1$, temos: $P(A\\cup B)=1-P(A\\cap B)$.<\/p>\n<p>Como $P(A\\cap B)$ pode n\u00e3o ser igual a 0 (zero), vem que $P(A\\cup B)$ pode n\u00e3o ser igual a 1.<\/p>\n<p>Consequentemente, $A\\cup B$ pode n\u00e3o ser um acontecimento certo.<\/p>\n<p>Assim, a afirma\u00e7\u00e3o dada \u00e9 falsa.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7073' onClick='GTTabs_show(0,7073)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seja S um espa\u00e7o de resultados, finito, associado a uma experi\u00eancia aleat\u00f3ria. Mostre que \u00e9 falsa a seguinte afirma\u00e7\u00e3o: \u00abQuaisquer que sejam os acontecimentos A e B, ($A\\subset S$ e $B\\subset&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19180,"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-7073","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":2406,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat71.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7073","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=7073"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7073\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19180"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7073"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}