{"id":34,"date":"2023-08-06T10:58:47","date_gmt":"2023-08-06T10:58:47","guid":{"rendered":"https:\/\/statorials.org\/tr\/birbirini-dislayan-olaylar\/"},"modified":"2023-08-06T10:58:47","modified_gmt":"2023-08-06T10:58:47","slug":"birbirini-dislayan-olaylar","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/birbirini-dislayan-olaylar\/","title":{"rendered":"Birbirini d\u0131\u015flayan etkinlikler"},"content":{"rendered":"<p>Burada birbirini d\u0131\u015flayan olaylar\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca birbirini d\u0131\u015flayan olaylar\u0131n \u00f6rneklerini ve bunlar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 da g\u00f6receksiniz. Son olarak, birbirini d\u0131\u015flayan etkinlikler ile di\u011fer etkinlik t\u00fcrleri aras\u0131ndaki farklar\u0131n neler oldu\u011funu \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-eventos-mutuamente-excluyentes\"><\/span> Birbirini d\u0131\u015flayan olaylar nelerdir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Birbirini d\u0131\u015flayan olaylar, ayn\u0131 anda ger\u00e7ekle\u015femeyen rastgele bir deneyin sonu\u00e7lar\u0131d\u0131r.<\/strong> Ba\u015fka bir deyi\u015fle, ortak tek bir olay olmad\u0131\u011f\u0131nda iki olay birbirini d\u0131\u015flar.<\/p>\n<p> Birbirini d\u0131\u015flayan olaylara ayn\u0131 zamanda <strong>birbirini d\u0131\u015flayan olaylar<\/strong> da denir.<\/p>\n<p> \u015eunu belirtmek gerekir ki, iki olay\u0131n birbirini d\u0131\u015flamas\u0131 i\u00e7in ayn\u0131 anda meydana gelmemesi yeterli de\u011fildir; e\u011fer bu t\u00fcr olaylar\u0131n ayn\u0131 anda meydana gelme ihtimali varsa, bunlar art\u0131k o t\u00fcrden olaylar de\u011fildir. \u0130ki olay\u0131n birbirini d\u0131\u015flamas\u0131 i\u00e7in, ortak ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131n\u0131n s\u0131f\u0131r olmas\u0131 gerekir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-eventos-mutuamente-excluyentes\"><\/span> Kar\u015f\u0131l\u0131kl\u0131 \u00d6zel Etkinliklere \u00d6rnekler<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Birbirini d\u0131\u015flayan olaylar\u0131n tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra, anlamlar\u0131n\u0131 tam olarak anlamak i\u00e7in a\u015fa\u011f\u0131da bu t\u00fcr olaylar\u0131n birka\u00e7 \u00f6rne\u011fini g\u00f6rebilirsiniz.<\/p>\n<p> \u00d6rne\u011fin, bir yaz\u0131-tura at\u0131\u015f\u0131ndaki <em>&#8220;tura&#8221;<\/em> ve <em>&#8220;yaz\u0131&#8221;<\/em> olaylar\u0131 hi\u00e7bir zaman ayn\u0131 anda ger\u00e7ekle\u015fmeyece\u011fi i\u00e7in birbirini d\u0131\u015flar.<\/p>\n<p> Zar at\u0131\u015f\u0131nda birbirini d\u0131\u015flayan olaylar\u0131n ba\u015fka \u00f6rneklerini de bulabiliriz. Bir zar\u0131 att\u0131\u011f\u0131m\u0131zda alt\u0131 olas\u0131 sonu\u00e7 vard\u0131r (1, 2, 3, 4, 5 ve 6), ancak yaln\u0131zca bir say\u0131 atabiliriz, dolay\u0131s\u0131yla alt\u0131 sonu\u00e7 birbirini d\u0131\u015flar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-de-eventos-mutuamente-excluyentes\"><\/span> Birbirini d\u0131\u015flayan olaylar\u0131n olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Birbirini d\u0131\u015flayan iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131 s\u0131f\u0131rd\u0131r<\/strong> \u00e7\u00fcnk\u00fc tan\u0131m gere\u011fi iki olay bir arada var olamaz. Dolay\u0131s\u0131yla birbirini d\u0131\u015flayan iki olay\u0131n kesi\u015fimi bo\u015f k\u00fcmedir.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0d8e7061e5e7c79e0ede9b1b5c072720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=\\varnothing\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00d6te yandan, <strong>bir olay\u0131n birbirini d\u0131\u015flayan bir \u00e7ift olaydan meydana gelme olas\u0131l\u0131\u011f\u0131, her bir olay\u0131n meydana gelme olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131d\u0131r<\/strong> .<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6b9b611e8eecce66db00b6a62c94c7a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cup B)=P(A)+P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"202\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Birbirini d\u0131\u015flayan iki olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in a\u015fa\u011f\u0131da size \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rma b\u0131rak\u0131yoruz.<\/p>\n<ul>\n<li> Bir kutuya 5 ye\u015fil, 4 sar\u0131 ve 2 mavi top koyuyoruz. Kutudan turuncu veya mavi bir topun \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> A\u00e7\u0131k\u00e7as\u0131, <em>&#8220;ye\u015fil top \u00e7ek&#8221;<\/em> , <em>&#8220;sar\u0131 top \u00e7ek&#8221;<\/em> ve <em>&#8220;mavi top \u00e7ek&#8221;<\/em> \u00fc\u00e7 olay\u0131 birbirini d\u0131\u015flar \u00e7\u00fcnk\u00fc ayn\u0131 anda ger\u00e7ekle\u015femezler. Bu nedenle <em>&#8220;ye\u015fil top veya mavi top \u00e7ekme&#8221;<\/em> olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in \u00f6nce iki olay\u0131n olas\u0131l\u0131klar\u0131n\u0131 ayr\u0131 ayr\u0131 hesaplamal\u0131, sonra bunlar\u0131 toplamal\u0131y\u0131z.<\/p>\n<p> B\u00f6ylece Laplace yasas\u0131n\u0131 uygulayarak kutudan ye\u015fil bir top \u00e7ekme olas\u0131l\u0131\u011f\u0131n\u0131 hesapl\u0131yoruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-68f6b4223a63448cf4e89485ee0ca28e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola verde})=\\cfrac{5}{5+4+2}=0,45\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"261\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Daha sonra mavi bir top elde etme olas\u0131l\u0131\u011f\u0131n\u0131 buluruz:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-89989b351db2440446982e836aebfee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola azuzl})=\\cfrac{2}{5+4+2}=0,18\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"260\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Yani ye\u015fil veya mavi bir topu yakalaman\u0131n toplam olas\u0131l\u0131\u011f\u0131, hesaplanan iki olas\u0131l\u0131\u011f\u0131n toplam\u0131 olacakt\u0131r: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9a14a263cfdb8c6e42e986652e918908_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(\\text{bola verde}\\cup \\text{bola azul})=\\\\[2ex] =P(\\text{bola verde})+P(\\text{bola azul})=\\\\[2ex] =0,45+0,18=0,63\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"93\" width=\"264\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"eventos-mutuamente-excluyentes-y-mutuamente-no-excluyentes\"><\/span>Birbirini d\u0131\u015flayan ve birbirini d\u0131\u015flayan olmayan olaylar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Mant\u0131ksal olarak, <strong>birbirini d\u0131\u015flayan olaylar ile kar\u015f\u0131l\u0131kl\u0131 olarak d\u0131\u015flay\u0131c\u0131 olmayan olaylar aras\u0131ndaki fark,<\/strong> bunlar\u0131n ayr\u0131cal\u0131kl\u0131 olmas\u0131d\u0131r. Birbirini d\u0131\u015flayan iki olay ayn\u0131 anda ger\u00e7ekle\u015femez, ancak birbirini d\u0131\u015flayan iki olay ayn\u0131 anda meydana gelebilir.<\/p>\n<p> \u00d6rne\u011fin, bir oyunda rastgele bir kart \u00e7ekerken, <em>&#8220;elmas kart \u00e7ek&#8221;<\/em> ve <em>&#8220;kalp kart \u00e7ek<\/em> &#8221; olaylar\u0131 birbirini d\u0131\u015flar, \u00e7\u00fcnk\u00fc hi\u00e7bir kart hem elmas kart hem de kalp kart\u0131 olamaz.<\/p>\n<p> Aksine, ayn\u0131 \u00f6rne\u011fi takip edersek, <em>&#8220;elmas kart \u00e7ek&#8221;<\/em> ve <em>&#8220;7&#8217;den k\u00fc\u00e7\u00fck say\u0131ya sahip bir kart \u00e7ek&#8221;<\/em> olaylar\u0131 birbirini d\u0131\u015flamaz \u00e7\u00fcnk\u00fc bu iki ko\u015fulu kar\u015f\u0131layan \u00e7ok say\u0131da kart vard\u0131r. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/birbirini-dislayan-olmayan-olaylar\/\">Kar\u015f\u0131l\u0131kl\u0131 M\u00fcnhas\u0131r Olmayan Etkinlikler<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"eventos-mutuamente-excluyentes-y-complementarios\"><\/span> Birbirini d\u0131\u015flayan ve tamamlay\u0131c\u0131 etkinlikler<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Birbirini d\u0131\u015flayan iki olay ile birbirini tamamlayan iki olay aras\u0131ndaki fark,<\/strong> bunlar\u0131n kolektif olarak d\u0131\u015flanan olaylar olup olmad\u0131\u011f\u0131d\u0131r. Birbirini d\u0131\u015flayan olaylar\u0131n kolektif olarak d\u0131\u015flay\u0131c\u0131 olmas\u0131 gerekmez, ancak tamamlay\u0131c\u0131 olaylar her zaman \u00f6yledir.<\/p>\n<p> Yani birbirini d\u0131\u015flayan iki olay, ayn\u0131 anda meydana gelemeyecekleri ancak yine de ba\u015fka bir olay\u0131n meydana gelebilece\u011fi bir deneyimin iki farkl\u0131 sonucudur. Aksine, iki olay, rastgele bir deneyin yaln\u0131zca iki olas\u0131 sonucu oldu\u011funda ve ayn\u0131 anda ger\u00e7ekle\u015femedi\u011finde tamamlay\u0131c\u0131d\u0131r.<\/p>\n<p> \u00d6rne\u011fin, bir zar\u0131n at\u0131lmas\u0131n\u0131 tamamlayan iki olay <em>, &#8220;3&#8217;ten k\u00fc\u00e7\u00fck veya ona e\u015fit bir say\u0131n\u0131n at\u0131lmas\u0131&#8221;<\/em> ve <em>&#8220;3&#8217;ten b\u00fcy\u00fck bir say\u0131n\u0131n at\u0131lmas\u0131&#8221;<\/em> olacakt\u0131r. Ancak birbirini d\u0131\u015flayan iki olay <em>&#8220;1 numaray\u0131 almak&#8221;<\/em> ve <em>&#8220;2 numaray\u0131 almak&#8221;<\/em> olacakt\u0131r, \u00e7\u00fcnk\u00fc bunlardan birinin ger\u00e7ekle\u015fmesi di\u011ferinin olamayaca\u011f\u0131 anlam\u0131na gelir, ancak yine de ayn\u0131 at\u0131\u015fta ba\u015fka say\u0131lar elde edebiliriz.<\/p>\n<p> Sonu\u00e7ta, <strong>t\u00fcm tamamlay\u0131c\u0131 olaylar birbirini d\u0131\u015flar<\/strong> , ancak birbirini d\u0131\u015flayan iki olay\u0131n mutlaka tamamlay\u0131c\u0131 olmas\u0131 gerekmez. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/zit-olay-tamamlayici-olay\/\">Ek etkinlikler<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"eventos-mutuamente-excluyentes-y-eventos-independientes\"><\/span> Birbirini d\u0131\u015flayan etkinlikler ve ba\u011f\u0131ms\u0131z etkinlikler<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bu b\u00f6l\u00fcmde birbirini d\u0131\u015flayan olaylar ile ba\u011f\u0131ms\u0131z olaylar aras\u0131ndaki farklar\u0131 a\u00e7\u0131klamak istiyoruz \u00e7\u00fcnk\u00fc bunlar olas\u0131l\u0131k ve istatistik \u00e7al\u0131\u015f\u0131rken a\u00e7\u0131k olmas\u0131 gereken iki kavramd\u0131r.<\/p>\n<p> <strong>Birbirini d\u0131\u015flayan olaylar ile ba\u011f\u0131ms\u0131z olaylar aras\u0131ndaki fark,<\/strong> birbirini d\u0131\u015flayan olaylar\u0131n ayn\u0131 anda meydana gelememesidir. Bunun yerine, ba\u011f\u0131ms\u0131z olaylar ayn\u0131 anda meydana gelebilir, ancak bir olay\u0131n olas\u0131l\u0131\u011f\u0131 di\u011ferini etkilemez.<\/p>\n<p> \u00d6rne\u011fin, bir para \u00fcst \u00fcste iki kez at\u0131ld\u0131\u011f\u0131nda, <em>&#8220;ilk at\u0131\u015fta tura&#8221;<\/em> ve <em>&#8220;ikinci at\u0131\u015fta tura&#8221;<\/em> olaylar\u0131 ba\u011f\u0131ms\u0131zd\u0131r \u00e7\u00fcnk\u00fc bir olay\u0131n meydana gelmesi di\u011fer olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 etkilemez. Ancak bu iki olay birbirini d\u0131\u015flamaz \u00e7\u00fcnk\u00fc her ikisi de ger\u00e7ekle\u015febilir.<\/p>\n<p> \u00d6te yandan, paray\u0131 yaln\u0131zca bir kez atarsak, <em>&#8220;tura&#8221;<\/em> ve <em>&#8220;yaz\u0131&#8221;<\/em> olaylar\u0131 art\u0131k birbirini d\u0131\u015flar \u00e7\u00fcnk\u00fc hi\u00e7bir zaman ayn\u0131 anda ger\u00e7ekle\u015fmeyecektir. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/olaylar-bagimsiz-olaylar\/\">Ba\u011f\u0131ms\u0131z Etkinlikler<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Burada birbirini d\u0131\u015flayan olaylar\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca birbirini d\u0131\u015flayan olaylar\u0131n \u00f6rneklerini ve bunlar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 da g\u00f6receksiniz. Son olarak, birbirini d\u0131\u015flayan etkinlikler ile di\u011fer etkinlik t\u00fcrleri aras\u0131ndaki farklar\u0131n neler oldu\u011funu \u00f6\u011freneceksiniz. Birbirini d\u0131\u015flayan olaylar nelerdir? Birbirini d\u0131\u015flayan olaylar, ayn\u0131 anda ger\u00e7ekle\u015femeyen rastgele bir deneyin sonu\u00e7lar\u0131d\u0131r. Ba\u015fka bir deyi\u015fle, ortak tek bir olay [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-34","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Birbirini d\u0131\u015flayan olaylar nelerdir? (\u00f6rnekler)<\/title>\n<meta name=\"description\" content=\"Birbirini d\u0131\u015flayan olaylar nelerdir ve bunlar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 nas\u0131l hesaplan\u0131r? 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