{"id":6983,"date":"2011-10-09T18:53:50","date_gmt":"2011-10-09T17:53:50","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6983"},"modified":"2022-01-25T12:49:41","modified_gmt":"2022-01-25T12:49:41","slug":"um-dado-tetraedrico","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6983","title":{"rendered":"Um dado tetra\u00e9drico"},"content":{"rendered":"<p><ul id='GTTabs_ul_6983' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6983' class='GTTabs_curr'><a  id=\"6983_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6983' ><a  id=\"6983_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_6983'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6985\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6985\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\" data-orig-size=\"218,222\" 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=\"Dado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\" class=\"alignright wp-image-6985 size-full\" title=\"Dado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\" alt=\"\" width=\"218\" height=\"222\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg 218w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado-147x150.jpg 147w\" sizes=\"auto, (max-width: 218px) 100vw, 218px\" \/><\/a>Considere a experi\u00eancia aleat\u00f3ria que consiste no lan\u00e7amento de um dado &#8220;perfeito&#8221; com a forma de um tetraedro, cujos v\u00e9rtices est\u00e3o numerados de 1 a 4, e anotar a pontua\u00e7\u00e3o do v\u00e9rtice voltado para cima.<\/p>\n<ol>\n<li>Qual \u00e9 o espa\u00e7o de resultados S?<\/li>\n<li>Escreva o conjunto de todos os subconjuntos de S.<\/li>\n<li>Indique a probabilidade dos acontecimentos:<\/li>\n<\/ol>\n<ul>\n<li>A: &#8220;sair pontua\u00e7\u00e3o menor que 2&#8221;;<\/li>\n<li>B: &#8220;sair pontua\u00e7\u00e3o n\u00e3o inferior a 2&#8221;.<\/li>\n<\/ul>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6983' onClick='GTTabs_show(1,6983)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6983'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>O espa\u00e7o de resultados da experi\u00eancia aleat\u00f3ria \u00e9 $S=\\left\\{ \\text{1}\\text{, 2}\\text{, 3}\\text{, 4} \\right\\}$.<br \/>\n\u00ad<\/li>\n<li>O conjunto de todos os subconjuntos de S \u00e9: \\[X=\\left\\{ \\varnothing ,\\left\\{ 1 \\right\\},\\left\\{ 2 \\right\\},\\left\\{ 3 \\right\\},\\left\\{ 4 \\right\\},\\left\\{ 1,2 \\right\\},\\left\\{ 1,3 \\right\\},\\left\\{ 1,4 \\right\\},\\left\\{ 2,3 \\right\\},\\left\\{ 2,4 \\right\\},\\left\\{ 3,4 \\right\\},\\left\\{ 1,2,3 \\right\\},\\left\\{ 1,2,4 \\right\\},\\left\\{ 1,3,4 \\right\\},\\left\\{ 2,3,4 \\right\\},\\left\\{ 1,2,3,4 \\right\\} \\right\\}\\]<\/li>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6985\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6985\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\" data-orig-size=\"218,222\" 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=\"Dado\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\" class=\"alignright wp-image-6985 size-full\" title=\"Dado\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg\" alt=\"\" width=\"218\" height=\"222\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado.jpg 218w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/4dado-147x150.jpg 147w\" sizes=\"auto, (max-width: 218px) 100vw, 218px\" \/><\/a>Ora, $A=\\left\\{ \\left\\{ 1 \\right\\} \\right\\}$.<br \/>\nComo $NCP=\\#S=4$ e $NCF=\\#A=1$, ent\u00e3o $p(A)=\\frac{1}{4}$.<\/p>\n<p>Ora, $B=\\left\\{ \\left\\{ 2 \\right\\},\\left\\{ 3 \\right\\},\\left\\{ 4 \\right\\} \\right\\}$.<br \/>\nComo $NCP=\\#S=4$ e $NCF=\\#B=3$, ent\u00e3o $p(B)=\\frac{3}{4}$.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6983' onClick='GTTabs_show(0,6983)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Considere a experi\u00eancia aleat\u00f3ria que consiste no lan\u00e7amento de um dado &#8220;perfeito&#8221; com a forma de um tetraedro, cujos v\u00e9rtices est\u00e3o numerados de 1 a 4, e anotar a pontua\u00e7\u00e3o do&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20956,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,217,216,215],"series":[],"class_list":["post-6983","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-espaco-de-resultados","tag-probabilidade"],"views":7611,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag164-4_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6983","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=6983"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6983\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20956"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6983"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6983"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6983"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6983"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}