{"id":7179,"date":"2011-11-20T19:01:58","date_gmt":"2011-11-20T19:01:58","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=7179"},"modified":"2022-01-25T20:06:09","modified_gmt":"2022-01-25T20:06:09","slug":"um-fabricante-de-bicicletas","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=7179","title":{"rendered":"Um fabricante de bicicletas"},"content":{"rendered":"<p><ul id='GTTabs_ul_7179' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_7179' class='GTTabs_curr'><a  id=\"7179_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_7179' ><a  id=\"7179_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_7179'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/bicicleta.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"7180\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=7180\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/bicicleta.jpg\" data-orig-size=\"251,201\" 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=\"Bicicleta\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/bicicleta.jpg\" class=\"alignright size-full wp-image-7180\" title=\"Bicicleta\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/bicicleta.jpg\" alt=\"\" width=\"151\" height=\"121\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/bicicleta.jpg 251w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/bicicleta-150x120.jpg 150w\" sizes=\"auto, (max-width: 151px) 100vw, 151px\" \/><\/a>Um fabricante de bicicletas atribui um c\u00f3digo de fabrico a cada bicicleta que produz.<\/p>\n<p>Cada c\u00f3digo \u00e9 formado por quatro algarismos (de 0 a 9) colocados por uma certa ordem.<\/p>\n<p>Escolhida uma bicicleta ao acaso, qual a probabilidade do seu c\u00f3digo ter exatamente tr\u00eas zeros?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_7179' onClick='GTTabs_show(1,7179)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_7179'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p>O c\u00f3digo \u00e9 constitu\u00eddo por 4 d\u00edgitos (\u2014 \u2014 \u2014 \u2014), podendo cada um deles ser escolhido de 10 maneiras diferentes, considerando os dez algarismos de 0 a 9. Logo o n\u00famero de casos poss\u00edveis \u00e9 $$NCP=10\\times 10\\times 10\\times 10={{10}^{4}}={}^{10}A{{&#8216;}_{4}}$$<\/p>\n<p>Os tr\u00eas algarismos &#8220;0&#8221; podem ser colocados em ${}^{4}{{C}_{3}}=4$ posi\u00e7\u00f5es diferentes (0\u00a00\u00a00 \u2014, 0 0 \u2014 0, 0 \u2014 0 0, \u2014 0 0 0) e, para cada uma destas disposi\u00e7\u00f5es,\u00a0o quarto d\u00edgito a posicionar pode ser escolhido de 9 maneiras distintas (os algarismos de 1 a 9). Logo, o n\u00famero de casos favor\u00e1veis \u00e9 $$NCF={}^{4}{{C}_{3}}\\times 9$$<\/p>\n<p>Portanto, a probabilidade pedida \u00e9 $$p=\\frac{{}^{4}{{C}_{3}}\\times 9}{{}^{10}A{{&#8216;}_{4}}}=\\frac{4\\times 9}{{{10}^{4}}}=\\frac{36}{10000}=\\frac{9}{2500}=0,0036$$<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_7179' onClick='GTTabs_show(0,7179)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um fabricante de bicicletas atribui um c\u00f3digo de fabrico a cada bicicleta que produz. Cada c\u00f3digo \u00e9 formado por quatro algarismos (de 0 a 9) colocados por uma certa ordem. Escolhida&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":21030,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[226,97,227],"tags":[427,255,215],"series":[],"class_list":["post-7179","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-analise-combinatoria","tag-probabilidade"],"views":2508,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/11\/12V1Pag173-39_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7179","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=7179"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/7179\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/21030"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=7179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=7179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=7179"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=7179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}