{"id":6949,"date":"2011-09-30T00:04:23","date_gmt":"2011-09-29T23:04:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6949"},"modified":"2022-01-16T02:58:20","modified_gmt":"2022-01-16T02:58:20","slug":"uma-caixa-com-8-bolas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6949","title":{"rendered":"Uma caixa com 8 bolas"},"content":{"rendered":"<p><ul id='GTTabs_ul_6949' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6949' class='GTTabs_curr'><a  id=\"6949_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6949' ><a  id=\"6949_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_6949'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6950\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6950\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3.jpg\" data-orig-size=\"375,307\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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=\"Caixa com bolas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3.jpg\" class=\"alignright size-medium wp-image-6950\" title=\"Caixa com bolas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3-300x245.jpg\" alt=\"\" width=\"180\" height=\"147\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3-300x245.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3-150x122.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9-pag27-3.jpg 375w\" sizes=\"auto, (max-width: 180px) 100vw, 180px\" \/><\/a>Uma caixa cont\u00e9m bolas pretas e bolas cor de laranja, num total de 8.<\/p>\n<p>A probabilidade de tirar da caixa uma bola preta sem olhar \u00e9 $\\frac{3}{8}$.<\/p>\n<ol>\n<li>Quantas bolas pretas existem na caixa?<\/li>\n<li>Quantas bolas cor de laranja existem na caixa?<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6949' onClick='GTTabs_show(1,6949)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6949'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como a caixa cont\u00e9m oito bolas, h\u00e1 8 possibilidades para extrair 1 bola.\u00a0Logo $NCP=8$.<br \/>\nSeja P o acontecimento &#8220;tirar uma bola preta&#8221;. Sabe-se que $P(P)=\\frac{3}{8}$.<br \/>\nAssim, temos: \\[\\begin{array}{*{35}{l}}<br \/>\nP(P)=\\frac{3}{8} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{NCF}{NCP}=\\frac{3}{8}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; \\frac{NCF}{8}=\\frac{3}{8}\u00a0 \\\\<br \/>\n{} &amp; \\Leftrightarrow\u00a0 &amp; NCF=3\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\nComo o n\u00famero de casos favor\u00e1veis ao acontecimento P: &#8220;tirar uma bola preta&#8221; \u00e9 3, ent\u00e3o h\u00e1 tr\u00eas bolas pretas na caixa.<br \/>\n\u00ad<\/li>\n<li>Como a caixa cont\u00e9m 8 bolas e as pretas s\u00e3o 3, ent\u00e3o h\u00e1 5 bolas cor de laranja na caixa.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6949' onClick='GTTabs_show(0,6949)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Uma caixa cont\u00e9m bolas pretas e bolas cor de laranja, num total de 8. A probabilidade de tirar da caixa uma bola preta sem olhar \u00e9 $\\frac{3}{8}$. Quantas bolas pretas existem&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20343,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,217,218,215],"series":[],"class_list":["post-6949","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-estatistica-e-probabilidades","tag-9-o-ano","tag-acontecimento","tag-espaco-de-acontecimentos","tag-probabilidade"],"views":4038,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9V1Pag027-3_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6949","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=6949"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6949\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20343"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6949"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6949"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}