{"id":7075,"date":"2011-10-16T19:27:04","date_gmt":"2011-10-16T18:27:04","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7075"},"modified":"2021-12-28T21:56:43","modified_gmt":"2021-12-28T21:56:43","slug":"calcule","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7075","title":{"rendered":"Calcule"},"content":{"rendered":"<p><ul id='GTTabs_ul_7075' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7075' class='GTTabs_curr'><a  id=\"7075_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7075' ><a  id=\"7075_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_7075'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Seja $\\Omega $ o espa\u00e7o de resultados associado a uma certa experi\u00eancia aleat\u00f3ria.<\/p>\n<p>Sejam A, B e C tr\u00eas acontecimentos ($A\\subset \\Omega $, $B\\subset \\Omega $ e $C\\subset \\Omega $) tais que $(A\\cup B)\\cap C=\\left\\{ {} \\right\\}$.<\/p>\n<p>Sabe-se que $P(A)=0,21$ e que $P(C)=0,47$.<\/p>\n<p>Calcule $P(A\\cup C)$, utilizando as propriedades das opera\u00e7\u00f5es com conjuntos e a axiom\u00e1tica das probabilidades.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7075' onClick='GTTabs_show(1,7075)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7075'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Sabe-se:<\/p>\n<ul>\n<li>$(A\\cup B)\\cap C=\\left\\{ {} \\right\\}$<\/li>\n<li>$P(A)=0,21$<\/li>\n<li>$P(C)=0,47$<\/li>\n<\/ul>\n<p>Como \u00e9 sabido, $P(A\\cup C)=P(A)+P(C)-P(A\\cap C)$\u00a0 (1).<\/p>\n<p>Aplicando a propriedade distributiva da interse\u00e7\u00e3o de conjuntos relativamente \u00e0 reuni\u00e3o de conjuntos e\u00a0tendo em conta que a reuni\u00e3o de dois conjuntos \u00e9\u00a0vazia se, e s\u00f3 se, os dois conjuntos forem vazios,\u00a0temos: \\[\\begin{array}{*{35}{l}}<br \/>\n(A\\cup B)\\cap C=\\left\\{ {} \\right\\} &amp; \\Leftrightarrow\u00a0 &amp; (A\\cap C)\\cup (B\\cap C)=\\left\\{ {} \\right\\}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\begin{matrix}<br \/>\nA\\cap C=\\left\\{ {} \\right\\} &amp; \\wedge\u00a0 &amp; B\\cap C=\\left\\{ {} \\right\\}\u00a0 \\\\<br \/>\n\\end{matrix}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Logo, sendo $A\\cap C=\\left\\{ {} \\right\\}$, de (1), vem: \\[\\begin{array}{*{35}{l}}<br \/>\nP(A\\cup C)=0,21+0,47-0 &amp; \\Leftrightarrow\u00a0 &amp; P(A\\cup C)=0,68\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7075' onClick='GTTabs_show(0,7075)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Seja $\\Omega $ o espa\u00e7o de resultados associado a uma certa experi\u00eancia aleat\u00f3ria. Sejam A, B e C tr\u00eas acontecimentos ($A\\subset \\Omega $, $B\\subset \\Omega $ e $C\\subset \\Omega $) tais&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14113,"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-7075","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":1933,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat55.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7075","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=7075"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7075\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14113"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7075"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7075"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7075"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7075"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}