{"id":6979,"date":"2011-10-09T17:23:38","date_gmt":"2011-10-09T16:23:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6979"},"modified":"2022-01-25T12:45:25","modified_gmt":"2022-01-25T12:45:25","slug":"a-ana-e-a-beatriz-disputam-um-torneio-de-tenis","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6979","title":{"rendered":"A Ana e a Beatriz disputam um torneio de t\u00e9nis"},"content":{"rendered":"<p><ul id='GTTabs_ul_6979' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6979' class='GTTabs_curr'><a  id=\"6979_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6979' ><a  id=\"6979_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_6979'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>A Ana e a Beatriz disputam um torneio de t\u00e9nis. A primeira que ganhar dois jogos seguidos ou que ganhar um total de tr\u00eas jogos, vence o torneio.<\/p>\n<p>Considere a experi\u00eancia aleat\u00f3ria que consiste em registar os resultados poss\u00edveis do torneio e identifique o espa\u00e7o de resultados que lhe est\u00e1 associado.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6979' onClick='GTTabs_show(1,6979)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6979'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>Comecemos por elaborar um diagrama de \u00e1rvore, de forma a identificarmos os resultados poss\u00edveis com facilidade.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/torneiotenis.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" title=\"Diagrama\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/torneiotenis.jpg\" alt=\"\" width=\"635\" height=\"328\" \/><\/a><\/p>\n<p>Portanto, o espa\u00e7o de resultados \u00e9:<br \/>\n$$S=\\left\\{ \\text{AA}\\text{, ABAA}\\text{, ABABA}\\text{, ABABB}\\text{, ABB}\\text{, BAA}\\text{, BABAA}\\text{, BABAB}\\text{, BABB}\\text{, BB} \\right\\}$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6979' onClick='GTTabs_show(0,6979)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A Ana e a Beatriz disputam um torneio de t\u00e9nis. A primeira que ganhar dois jogos seguidos ou que ganhar um total de tr\u00eas jogos, vence o torneio. Considere a experi\u00eancia&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20955,"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],"series":[],"class_list":["post-6979","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"],"views":1571,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/12V1Pag164-2_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6979","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=6979"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6979\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20955"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6979"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6979"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6979"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6979"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}