{"id":393,"date":"2023-08-01T05:30:46","date_gmt":"2023-08-01T05:30:46","guid":{"rendered":"https:\/\/statorials.org\/tr\/olaylarin-kesisme-olasiligi\/"},"modified":"2023-08-01T05:30:46","modified_gmt":"2023-08-01T05:30:46","slug":"olaylarin-kesisme-olasiligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olaylarin-kesisme-olasiligi\/","title":{"rendered":"Olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131"},"content":{"rendered":"<p>Bu makalede olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen al\u0131\u015ft\u0131rmalar\u0131 \u00f6\u011freneceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-interseccion-de-sucesos\"><\/span> Olaylar\u0131n kesi\u015fimi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k teorisinde <strong>olaylar\u0131n kesi\u015fmesi<\/strong> , sonucu operasyonun t\u00fcm olaylar\u0131nda ortak olan temel olaylardan olu\u015fan olaylar\u0131n bir operasyonudur. Yani A ve B olaylar\u0131n\u0131n kesi\u015fimi, ayn\u0131 anda A ve B&#8217;ye ait olan t\u00fcm olaylar\u0131n birle\u015fiminden olu\u015fur.<\/p>\n<p> \u0130ki olay\u0131n kesi\u015fimi \u22c2 sembol\u00fc ile ifade edilir. B\u00f6ylece A ve B olaylar\u0131n\u0131n kesi\u015fimi A\u22c2B olarak yaz\u0131l\u0131r.<\/p>\n<p> \u00d6rne\u011fin, bir zar\u0131n rastgele at\u0131lmas\u0131 deneyinde, e\u011fer bir olay bir \u00e7ift say\u0131n\u0131n A={2, 4, 6} at\u0131lmas\u0131ysa ve ba\u015fka bir olay da \u00fc\u00e7ten b\u00fcy\u00fck bir say\u0131n\u0131n B={4, 5 at\u0131lmas\u0131ysa, 6 } ise iki olay\u0131n kesi\u015fimi A\u22c2B={4, 6}&#8217;t\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-de-la-interseccion-de-sucesos\"><\/span> Olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131 form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0130ki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131,<\/strong> bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ile ilk olay g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda di\u011fer olay\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir.<\/p>\n<p> Bu nedenle, <strong>iki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131 form\u00fcl\u00fc<\/strong> P(A\u22c2B)=P(A) P(B|A)=P(B) P(A|B) \u015feklindedir.<\/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-acadb606c53d2237406ab492ad5c26ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=P(A)\\cdot P(B|A)=P(B)\\cdot P(A|B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:7px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c74288aabc0e2ca280d25d92bf1a1ec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> Bunlar iki ba\u011f\u0131ml\u0131 olayd\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5e28c16735c6423d27941ce417b5fb4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> A olay\u0131 ile B olay\u0131n\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f0e9e218bb5d81f21881e6c57e37c7a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"40\" style=\"vertical-align: -5px;\"><\/p>\n<p> A olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4c0c4ce70731e4b1321acc93f53679ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B|A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<p> A olay\u0131 verildi\u011finde B olay\u0131n\u0131n meydana gelme ko\u015fullu olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3cf84b3bfcc955798a43fce91458ff42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p> B olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-aa17d530df1f8fd53a077cb6af545add_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A|B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"59\" style=\"vertical-align: -5px;\"><\/p>\n<p> verilen B olay\u0131n\u0131n meydana gelmesinin ko\u015fullu olas\u0131l\u0131\u011f\u0131d\u0131r. <\/li>\n<\/ul>\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\/kosullu-kosullu-olasilik\/\">Ko\u015fullu olas\u0131l\u0131k (veya ko\u015fullu olas\u0131l\u0131k)<\/a><\/div>\n<p> Ancak iki olay ba\u011f\u0131ms\u0131zsa bu, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n di\u011fer olay\u0131n meydana gelip gelmemesine ba\u011fl\u0131 olmad\u0131\u011f\u0131 anlam\u0131na gelir. Bu nedenle iki ba\u011f\u0131ms\u0131z olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131 form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/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-593a1a131cab23d805d8324e21e6b4ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=P(A)\\cdot P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:7px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-816b613a4f79d4bf9cb51396a9654120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> Ve<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c74288aabc0e2ca280d25d92bf1a1ec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> Bunlar iki ba\u011f\u0131ms\u0131z olayd\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5e28c16735c6423d27941ce417b5fb4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> A olay\u0131 ile B olay\u0131n\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f0e9e218bb5d81f21881e6c57e37c7a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"40\" style=\"vertical-align: -5px;\"><\/p>\n<p> A olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li style=\"margin-bottom:8px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3cf84b3bfcc955798a43fce91458ff42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p> B olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131d\u0131r. <\/li>\n<\/ul>\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<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-resueltos-de-la-probabilidad-de-la-interseccion-de-sucesos\"><\/span> Olay kesi\u015fme olas\u0131l\u0131\u011f\u0131na ili\u015fkin ger\u00e7ek d\u00fcnyadan \u00f6rnekler<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Daha sonra size ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f iki \u00f6rnek b\u0131rak\u0131yoruz, b\u00f6ylece iki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilirsiniz. \u00d6nce iki ba\u011f\u0131ms\u0131z olay\u0131n, sonra da iki ba\u011f\u0131ml\u0131 olay\u0131n kesi\u015fimine ili\u015fkin bir \u00f6rnek g\u00f6rece\u011fiz, b\u00f6ylece her iki durumu da g\u00f6rebilirsiniz. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-de-la-interseccion-de-dos-sucesos-independientes\"><\/span> \u0130ki ba\u011f\u0131ms\u0131z olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Art arda \u00fc\u00e7 kez \u00e7ekili\u015f ba\u015flat\u0131l\u0131r. Her \u00fc\u00e7 at\u0131\u015fta da tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bulun.<\/li>\n<\/ul>\n<p> Bu durumda ortak olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak istedi\u011fimiz olaylar ba\u011f\u0131ms\u0131zd\u0131r \u00e7\u00fcnk\u00fc bir \u00e7ekili\u015fin sonucu bir \u00f6nceki \u00e7ekili\u015fte elde edilen sonuca ba\u011fl\u0131 de\u011fildir. Bu nedenle, ard\u0131 ard\u0131na \u00fc\u00e7 tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in ba\u011f\u0131ms\u0131z olaylara ili\u015fkin kesi\u015fim olas\u0131l\u0131\u011f\u0131 form\u00fcl\u00fcn\u00fc kullanmal\u0131y\u0131z:<\/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-593a1a131cab23d805d8324e21e6b4ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=P(A)\\cdot P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kura \u00e7ekerken yaln\u0131zca iki olas\u0131 sonu\u00e7 vard\u0131r; tura veya yaz\u0131 gelebilir. Buna g\u00f6re, bir para at\u0131ld\u0131\u011f\u0131nda yaz\u0131 veya tura gelme olas\u0131l\u0131\u011f\u0131:<\/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-24700638f62e83613a39f2b566e2fb9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara})=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dolay\u0131s\u0131yla, \u00fc\u00e7 yaz\u0131 tura at\u0131\u015f\u0131nda da tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in, tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 \u00fc\u00e7le \u00e7arpmam\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-54abe4c41545eb6e46fd1cf97f8a3253_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{cara}\\cap \\text{cara}\\cap \\text{cara})&amp;=P(\\text{cara})\\cdot P(\\text{cara})\\cdot P(\\text{cara})\\\\[2ex]&amp;=0,5\\cdot 0,5\\cdot 0,5\\\\[2ex]&amp;=0,125\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"394\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> K\u0131sacas\u0131 art arda \u00fc\u00e7 kez tura gelme olas\u0131l\u0131\u011f\u0131 %12,5&#8217;tir. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-de-la-interseccion-de-dos-sucesos-dependientes\"><\/span> \u0130ki ba\u011f\u0131ml\u0131 olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Bo\u015f bir kutuya 8 mavi top, 4 turuncu top ve 2 ye\u015fil top koyuyoruz. \u0130lk \u00e7ekilen topu kutuya geri koymadan \u00f6nce bir top, sonra ba\u015fka bir top \u00e7ekersek, ilk topun mavi, ikinci topun turuncu olma olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Bu durumda olaylar ba\u011f\u0131ml\u0131d\u0131r \u00e7\u00fcnk\u00fc ikinci \u00e7ekili\u015fte turuncu bir top alma olas\u0131l\u0131\u011f\u0131, ilk \u00e7ekili\u015fte \u00e7ekilen topun rengine ba\u011fl\u0131d\u0131r. Bu nedenle, problemin bize sordu\u011fu olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in ba\u011f\u0131ml\u0131 olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131 form\u00fcl\u00fcn\u00fc kullanmal\u0131y\u0131z:<\/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> \u0130lk \u00e7ekili\u015fte mavi top alma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek kolayd\u0131r; mavi toplar\u0131n say\u0131s\u0131n\u0131 toplam top say\u0131s\u0131na b\u00f6lmeniz yeterlidir:<\/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-01c2ac51c56664735750a0821834727d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola azul})=\\cfrac{8}{8+4+2}=\\cfrac{8}{14}=0,57\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"295\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> \u00d6te yandan, mavi bir top ald\u0131ktan sonra turuncu bir top \u00e7ekme olas\u0131l\u0131\u011f\u0131, turuncu toplar\u0131n say\u0131s\u0131 farkl\u0131 oldu\u011fundan ve ayr\u0131ca kutunun i\u00e7inde art\u0131k bir top eksildi\u011finden farkl\u0131 \u015fekilde hesaplan\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-a4dfda0193e549c67dabe2e6065d84f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola naranja}|\\text{bola azul})=\\cfrac{4}{7+4+2}=\\cfrac{4}{13}=0,31\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"397\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> B\u00f6ylece \u00f6nce mavi, sonra turuncu top \u00e7ekme olas\u0131l\u0131\u011f\u0131 yukar\u0131da bulunan iki olas\u0131l\u0131\u011f\u0131n \u00e7arp\u0131lmas\u0131yla hesaplan\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-94896f8575aeb7e73cc056595920fedb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(\\text{bola azul}\\cap\\text{bola naranja})=\\\\[2ex]=P(\\text{bola azul})\\cdot P(\\text{bola naranja}|\\text{bola azul})=\\\\[2ex]=0,57\\cdot 0,31= \\\\[2ex]=0,18\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"130\" width=\"348\" style=\"vertical-align: 0px;\"><\/p>\n<\/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\/olaylarin-birlesme-olasiligi\/\">Olaylar\u0131n birle\u015fme olas\u0131l\u0131\u011f\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-interseccion-de-sucesos\"><\/span> Olay Kav\u015fak \u00d6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k teorisinde olaylar\u0131n kesi\u015fimi a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>De\u011fi\u015fme \u00f6zelli\u011fi:<\/strong> Kesi\u015fme olaylar\u0131n\u0131n s\u0131ras\u0131 i\u015flemin sonucunu de\u011fi\u015ftirmez.<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf8f77ee754a8baedd35ff8cd79fbbd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cap B=B\\cap A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"118\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0130li\u015fkisel \u00f6zellik:<\/strong> Sonu\u00e7 ayn\u0131 oldu\u011fundan, \u00fc\u00e7 olay\u0131n kesi\u015fimi herhangi bir s\u0131rayla hesaplanabilir.<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fb1da58ec6bf1f24f459a5edf91507eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(A\\cap B)\\cap C=A\\cap (B\\cap C)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"211\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li> <span style=\"color:#101010;font-weight: normal;\"><strong>Da\u011f\u0131t\u0131c\u0131 \u00f6zellik:<\/strong> Olaylar\u0131n kesi\u015fimi, olaylar\u0131n birle\u015fimindeki da\u011f\u0131t\u0131c\u0131 \u00f6zelli\u011fi kar\u015f\u0131lar.<\/span> <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e43f1e4d6e688179f911a63ac3b46789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cap (B\\cup C)=(A\\cap B)\\cup (A\\cap C)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"259\" style=\"vertical-align: -5px;\"><\/p>\n<\/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\/etkinliklerle-yapilan-islemler\/\">Olaylarla yap\u0131lan i\u015flemler<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen al\u0131\u015ft\u0131rmalar\u0131 \u00f6\u011freneceksiniz. Olaylar\u0131n kesi\u015fimi nedir? Olas\u0131l\u0131k teorisinde olaylar\u0131n kesi\u015fmesi , sonucu operasyonun t\u00fcm olaylar\u0131nda ortak olan temel olaylardan olu\u015fan olaylar\u0131n bir operasyonudur. Yani A ve B olaylar\u0131n\u0131n kesi\u015fimi, ayn\u0131 anda A ve B&#8217;ye ait olan [&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-393","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 Olaylar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131<\/title>\n<meta name=\"description\" content=\"Burada olay kesi\u015fmesinin ne oldu\u011funu, olay kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 (form\u00fcl) ve \u00e7\u00f6z\u00fcml\u00fc \u00f6rnekleri \u00f6\u011freneceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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