{"id":31,"date":"2023-08-06T13:04:39","date_gmt":"2023-08-06T13:04:39","guid":{"rendered":"https:\/\/statorials.org\/tr\/olaylara-bagli-olaylar\/"},"modified":"2023-08-06T13:04:39","modified_gmt":"2023-08-06T13:04:39","slug":"olaylara-bagli-olaylar","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olaylara-bagli-olaylar\/","title":{"rendered":"Ba\u011f\u0131ml\u0131 olaylar (veya ba\u011f\u0131ml\u0131 olaylar)"},"content":{"rendered":"<p>Bu sayfada ba\u011f\u0131ml\u0131 olaylar olarak da adland\u0131r\u0131lan ba\u011f\u0131ml\u0131 olaylar\u0131n ne oldu\u011funu ve bu t\u00fcr olaylar\u0131n birka\u00e7 \u00f6rne\u011fini g\u00f6receksiniz. Ek olarak, iki veya daha fazla ba\u011f\u0131ml\u0131 olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 ve ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z olaylar aras\u0131ndaki farklar\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 da \u00f6\u011fretiyoruz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-los-eventos-dependientes\"><\/span> Ba\u011f\u0131ml\u0131 olaylar nelerdir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ba\u011f\u0131ml\u0131 olaylar, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olan rastgele bir deneyin sonu\u00e7lar\u0131d\u0131r<\/strong> . Yani, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 di\u011fer olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 etkiliyorsa iki olay ba\u011f\u0131ml\u0131d\u0131r.<\/p>\n<p> Ba\u011f\u0131ml\u0131 olaylara ayn\u0131 zamanda <strong>ba\u011f\u0131ml\u0131 olaylar<\/strong> da denir.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-eventos-dependientes\"><\/span> Ba\u011f\u0131ml\u0131 olaylara \u00f6rnekler<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ba\u011f\u0131ml\u0131 olaylar\u0131n (veya ba\u011f\u0131ml\u0131 olaylar\u0131n) tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra, bu t\u00fcr olaylar\u0131n birka\u00e7 \u00f6rne\u011fini burada bulabilirsiniz. Ama\u00e7, ba\u011f\u0131ml\u0131 olaylar\u0131n anlam\u0131n\u0131 tam olarak anlaman\u0131zd\u0131r, bu nedenle herhangi bir sorunuz varsa bunlar\u0131 a\u015fa\u011f\u0131da yorumlarda sorabilirsiniz.<\/p>\n<p> \u00d6rne\u011fin, ayn\u0131 desteden art arda iki kart \u00e7ekmek iki ba\u011f\u0131ml\u0131 olayd\u0131r, \u00e7\u00fcnk\u00fc pakette bir kart eksik oldu\u011fu i\u00e7in ikinci \u00e7ekili\u015fte <em>&#8220;karo 3&#8217;\u00fcn\u00fc \u00e7ekme&#8221;<\/em> olas\u0131l\u0131\u011f\u0131 ilk \u00e7ekili\u015fe g\u00f6re daha y\u00fcksektir. \u00d6te yandan, s\u00f6z konusu kart\u0131n ikinci \u00e7\u0131karma s\u0131ras\u0131nda \u00e7ekilme olas\u0131l\u0131\u011f\u0131, e\u011fer kart birinci \u00e7\u0131karma s\u0131ras\u0131nda zaten \u00e7ekilmi\u015fse s\u0131f\u0131rd\u0131r. Dolay\u0131s\u0131yla ikinci olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 birinci olay\u0131n sonucuna ba\u011fl\u0131d\u0131r.<\/p>\n<p> Ba\u011f\u0131ml\u0131 olaylara bir ba\u015fka \u00f6rnek de, \u015firketin son bir y\u0131lda elde etti\u011fi ekonomik k\u00e2ra ba\u011fl\u0131 olarak borsada belirli hisse senetlerinin fiyat\u0131n\u0131n artmas\u0131 veya azalmas\u0131d\u0131r. Prensip olarak, \u015firket k\u00e2r ediyorsa fiyat\u0131n y\u00fckselme olas\u0131l\u0131\u011f\u0131 daha y\u00fcksektir, ancak \u015firket zarar ediyorsa hisse senedi fiyat\u0131n\u0131n d\u00fc\u015fme olas\u0131l\u0131\u011f\u0131 daha y\u00fcksektir.<\/p>\n<p> K\u0131sacas\u0131, <strong>ba\u011f\u0131ml\u0131 olaylar \u00f6nceki olaylardan etkilenir<\/strong> , \u00e7\u00fcnk\u00fc ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 \u00f6nceki sonu\u00e7lara ba\u011fl\u0131d\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-de-eventos-dependientes\"><\/span> Ba\u011f\u0131ml\u0131 olaylar\u0131n olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0130ki ba\u011f\u0131ml\u0131 A ve B olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131,<\/strong> A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 ile A olay\u0131 verildi\u011finde B olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir.<\/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-dddb39f8c7ff49e40025c3aae59044d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=P(A)\\cdot P(B|A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"211\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00d6rnek olarak iki ba\u011f\u0131ml\u0131 olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayaca\u011f\u0131z. Alt\u0131 ye\u015fil top ve \u00fc\u00e7 sar\u0131 topun bulundu\u011fu bir kutudan iki ye\u015fil topun arka arkaya al\u0131nmas\u0131na dayanarak olaylar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 belirleyece\u011fiz.<\/p>\n<p> \u0130kinci denemede ye\u015fil top \u00e7ekme olas\u0131l\u0131\u011f\u0131, ilk denemede ye\u015fil topun veya sar\u0131 topun \u00e7ekilmesine ba\u011fl\u0131d\u0131r, dolay\u0131s\u0131yla bunlar asl\u0131nda iki ba\u011f\u0131ml\u0131 olayd\u0131r.<\/p>\n<p> \u0130lk olarak, Laplace yasas\u0131n\u0131 kullanarak ilk denemede ye\u015fil 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-112f8c345e143e90aa7ceb9e95940c44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{verde})=\\cfrac{6}{9}=0,67\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"162\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Daha sonra, kutudan ye\u015fil bir top \u00e7ektikten sonra ba\u015fka bir ye\u015fil top \u00e7ekme olas\u0131l\u0131\u011f\u0131n\u0131 hesapl\u0131yoruz. Bu olay\u0131n olas\u0131l\u0131\u011f\u0131 \u00f6nceki sonuca ba\u011fl\u0131 oldu\u011fundan, ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fcn\u00fc uygulamam\u0131z gerekir:<\/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-4baad25a13a859703f021bf454cb8530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{verde}|\\text{verde})=\\cfrac{5}{8}=0,63\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"208\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle, iki ba\u011f\u0131ml\u0131 olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131, birinci olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n ikinci olay\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131 ile \u00e7arp\u0131m\u0131d\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-0d664ff9de39c69b078fc79dd4e8f123_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(\\text{verde}\\cap \\text{verde})=\\\\[2ex]=P(\\text{verde})\\cdot P(\\text{verde}|\\text{verde})=\\\\[1ex] =\\cfrac{6}{9}\\cdot \\cfrac{5}{8}=\\cfrac{5}{12}=0,42\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"234\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"eventos-dependientes-e-independientes\"><\/span> Ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z olaylar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ba\u011f\u0131ml\u0131 olaylar ile ba\u011f\u0131ms\u0131z olaylar aras\u0131ndaki fark,<\/strong> ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na ba\u011f\u0131ml\u0131l\u0131kt\u0131r. Bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 di\u011fer olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 do\u011furuyorsa iki olay ba\u011f\u0131ml\u0131d\u0131r; bir olay\u0131n olas\u0131l\u0131\u011f\u0131 olay\u0131n meydana gelip gelmemesine ba\u011fl\u0131 olmad\u0131\u011f\u0131nda ise iki olay ba\u011f\u0131ms\u0131zd\u0131r. di\u011fer olay.<\/p>\n<p> \u00d6rne\u011fin, bir torbaya d\u00f6rt siyah top ve yedi beyaz top koyarsak, \u00f6nce siyah top, sonra beyaz top \u00e7ekme olaylar\u0131, ilk topu torbaya geri koyup koymamam\u0131za ba\u011fl\u0131 olarak birbirine ba\u011fl\u0131 olacakt\u0131r. .<\/p>\n<p> Ba\u011f\u0131ms\u0131z olaylar\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131, ba\u011f\u0131ml\u0131 olaylara g\u00f6re farkl\u0131 \u015fekilde hesaplan\u0131r. Burada nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz: <\/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 olaylar\u0131n olas\u0131l\u0131\u011f\u0131<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu sayfada ba\u011f\u0131ml\u0131 olaylar olarak da adland\u0131r\u0131lan ba\u011f\u0131ml\u0131 olaylar\u0131n ne oldu\u011funu ve bu t\u00fcr olaylar\u0131n birka\u00e7 \u00f6rne\u011fini g\u00f6receksiniz. Ek olarak, iki veya daha fazla ba\u011f\u0131ml\u0131 olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 ve ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z olaylar aras\u0131ndaki farklar\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131 da \u00f6\u011fretiyoruz. Ba\u011f\u0131ml\u0131 olaylar nelerdir? Ba\u011f\u0131ml\u0131 olaylar, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olan rastgele bir deneyin sonu\u00e7lar\u0131d\u0131r . Yani, bir [&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-31","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 Ba\u011f\u0131ml\u0131 olaylar (veya ba\u011f\u0131ml\u0131 olaylar)<\/title>\n<meta name=\"description\" content=\"Ba\u011f\u0131ml\u0131 olaylar (veya ba\u011f\u0131ml\u0131 olaylar) nelerdir, ba\u011f\u0131ml\u0131 olaylara \u00f6rnekler ve ba\u011f\u0131ml\u0131 olaylar\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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