{"id":6935,"date":"2011-09-27T01:22:18","date_gmt":"2011-09-27T00:22:18","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6935"},"modified":"2022-01-16T02:24:39","modified_gmt":"2022-01-16T02:24:39","slug":"uma-caixa-contem-bolas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6935","title":{"rendered":"Uma caixa cont\u00e9m bolas"},"content":{"rendered":"<p><ul id='GTTabs_ul_6935' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6935' class='GTTabs_curr'><a  id=\"6935_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6935' ><a  id=\"6935_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_6935'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6936\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6936\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg\" data-orig-size=\"469,332\" 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=\"Bolas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg\" class=\"alignright size-medium wp-image-6936\" title=\"Bolas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-300x212.jpg\" alt=\"\" width=\"210\" height=\"148\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-300x212.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-150x106.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-400x283.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg 469w\" sizes=\"auto, (max-width: 210px) 100vw, 210px\" \/><\/a>Uma caixa cont\u00e9m 6 bolas vermelhas, 5 verdes, 8 azuis e 3 amarelas.<\/p>\n<p>Determina a probabilidade de, escolhendo uma bola ao acaso, ela ser:<\/p>\n<ol>\n<li>verde;<\/li>\n<li>vermelha;<\/li>\n<li>amarela;<\/li>\n<li>azul.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6935' onClick='GTTabs_show(1,6935)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6935'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>No sentido de distinguir as bolas da mesma cor, vamos numer\u00e1-las.<\/p>\n<p>O conjunto de todos os resultados poss\u00edveis (equiprov\u00e1veis) nesta experi\u00eancia aleat\u00f3ria (espa\u00e7o de resultados) \u00e9: \\[S=\\left\\{ {{E}_{1}},{{E}_{2}},{{E}_{3}},{{E}_{4}},{{E}_{5}},{{E}_{6}},{{V}_{1}},{{V}_{2}},{{V}_{3}},{{V}_{4}},{{V}_{5}},{{Z}_{1}},{{Z}_{2}},{{Z}_{3}},{{Z}_{4}},{{Z}_{5}},{{Z}_{6}},{{Z}_{7}},{{Z}_{8}},{{A}_{1}},{{A}_{2}},{{A}_{3}} \\right\\}\\]<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6936\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6936\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg\" data-orig-size=\"469,332\" 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=\"Bolas\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg\" class=\"alignright size-medium wp-image-6936\" title=\"Bolas\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-300x212.jpg\" alt=\"\" width=\"210\" height=\"148\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-300x212.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-150x106.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas-400x283.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/caixabolas.jpg 469w\" sizes=\"auto, (max-width: 210px) 100vw, 210px\" \/><\/a>Portanto, nesta experi\u00eancia aleat\u00f3ria, o n\u00famero de casos poss\u00edveis \u00e9: $NCP=\\#S=22$.<\/p>\n<ol>\n<li>Consideremos o acontecimento X: &#8220;extrair uma bola verde&#8221;.<br \/>\nComo $X=\\left\\{ {{V}_{1}},{{V}_{2}},{{V}_{3}},{{V}_{4}},{{V}_{5}} \\right\\}$ \u00e9 o conjunto de resultados favor\u00e1veis a este acontecimento, ent\u00e3o $NCF=\\#X=5$.<br \/>\nLogo, $P(&#8221;extrair\\,\\,uma\\,\\,bola\\,\\,verde&#8221;)=P(X)=\\frac{5}{22}$.<br \/>\n\u00ad<\/li>\n<li>Consideremos o acontecimento Y: &#8220;extrair uma bola vermelha&#8221;.<br \/>\nComo\u00a0$Y=\\left\\{ {{E}_{1}},{{E}_{2}},{{E}_{3}},{{E}_{4}},{{E}_{5}},{{E}_{6}} \\right\\}$ \u00e9 o conjunto de resultados favor\u00e1veis a este acontecimento, ent\u00e3o $NCF=\\#Y=6$.<br \/>\nLogo, $P(&#8221;extrair\\,\\,uma\\,\\,bola\\,\\,vermelha&#8221;)=P(Y)=\\frac{6}{22}=\\frac{3}{11}$.<br \/>\n\u00ad<\/li>\n<li>Consideremos o acontecimento W: &#8220;extrair uma bola amarela&#8221;.<br \/>\nComo\u00a0$W=\\left\\{ {{A}_{1}},{{A}_{2}},{{A}_{3}} \\right\\}$ \u00e9 o conjunto de resultados favor\u00e1veis a este acontecimento, ent\u00e3o $NCF=\\#W=3$.<br \/>\nLogo, $P(&#8221;extrair\\,\\,uma\\,\\,bola\\,\\,amarela&#8221;)=P(W)=\\frac{3}{22}$.<br \/>\n\u00ad<\/li>\n<li>Consideremos o acontecimento W: &#8220;extrair uma bola azul&#8221;.<br \/>\nComo\u00a0$K=\\left\\{ {{Z}_{1}},{{Z}_{2}},{{Z}_{3}},{{Z}_{4}},{{Z}_{5}},{{Z}_{6}},{{Z}_{7}},{{Z}_{8}} \\right\\}$ \u00e9 o conjunto de resultados favor\u00e1veis a este acontecimento, ent\u00e3o $NCF=\\#K=8$.<br \/>\nLogo, $P(&#8221;extrair\\,\\,uma\\,\\,bola\\,\\,azul&#8221;)=P(K)=\\frac{8}{22}=\\frac{4}{11}$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6935' onClick='GTTabs_show(0,6935)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Uma caixa cont\u00e9m 6 bolas vermelhas, 5 verdes, 8 azuis e 3 amarelas. Determina a probabilidade de, escolhendo uma bola ao acaso, ela ser: verde; vermelha; amarela; azul. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20338,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,214],"tags":[426,217,216,215],"series":[],"class_list":["post-6935","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-resultados","tag-probabilidade"],"views":3400,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/09\/9V1Pag022-13_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6935","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=6935"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6935\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20338"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6935"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}