{"id":7064,"date":"2011-10-16T01:17:20","date_gmt":"2011-10-16T00:17:20","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7064"},"modified":"2022-01-25T17:42:22","modified_gmt":"2022-01-25T17:42:22","slug":"a-probabilidade-de-amanha-chover","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7064","title":{"rendered":"A probabilidade de amanh\u00e3 chover"},"content":{"rendered":"<p><ul id='GTTabs_ul_7064' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7064' class='GTTabs_curr'><a  id=\"7064_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7064' ><a  id=\"7064_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_7064'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/weather.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7065\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7065\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/weather.png\" data-orig-size=\"200,200\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"O tempo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/weather.png\" class=\"alignright size-full wp-image-7065\" title=\"O tempo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/weather.png\" alt=\"\" width=\"120\" height=\"120\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/weather.png 200w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/weather-150x150.png 150w\" sizes=\"auto, (max-width: 120px) 100vw, 120px\" \/><\/a>Segundo um especialista em meteorologia, a probabilidade de amanh\u00e3 chover \u00e9 tr\u00eas vezes maior do que a de estar enevoado e esta \u00e9 dupla da de estar sol.<\/p>\n<p>Supondo que existem apenas estas possibilidades, qual \u00e9, ent\u00e3o,\u00a0a probabilidade de amanh\u00e3 chover?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7064' onClick='GTTabs_show(1,7064)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7064'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Sejam C: &#8220;Amanh\u00e3 chover&#8221;, E: &#8220;Amanh\u00e3 estar enevoado&#8221; e L: &#8220;Amanh\u00e3 estar sol&#8221;.<\/p>\n<p>Sabe-se:<\/p>\n<ul>\n<li>$P(C)=3P(E)$<\/li>\n<li>$P(E)=2P(L)$<\/li>\n<li>$C\\cup E\\cup L=S$<\/li>\n<\/ul>\n<p>Admitindo que os acontecimentos s\u00e3o disjuntos dois a dois, temos: $P(C\\cup E\\cup L)=P(C)+P(E)+P(L)=P(S)=1$.<\/p>\n<p>Sendo $P(L)=p$, temos: \\[\\begin{array}{*{35}{l}}<br \/>\n6p+2p+p=1 &amp; \\Leftrightarrow\u00a0 &amp; 9p=1\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; p=\\frac{1}{9}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Logo, a probabilidade de amanh\u00e3 chover \u00e9 $P(C)=6\\times \\frac{1}{9}=\\frac{2}{3}$.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7064' onClick='GTTabs_show(0,7064)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Segundo um especialista em meteorologia, a probabilidade de amanh\u00e3 chover \u00e9 tr\u00eas vezes maior do que a de estar enevoado e esta \u00e9 dupla da de estar sol. Supondo que existem&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20998,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,217,215],"series":[],"class_list":["post-7064","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-acontecimento","tag-probabilidade"],"views":1421,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag172-31_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7064","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=7064"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7064\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20998"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7064"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7064"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7064"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7064"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}