{"id":1343,"date":"2023-07-26T19:24:24","date_gmt":"2023-07-26T19:24:24","guid":{"rendered":"https:\/\/statorials.org\/tr\/a-ve-b-olasiligi\/"},"modified":"2023-07-26T19:24:24","modified_gmt":"2023-07-26T19:24:24","slug":"a-ve-b-olasiligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/a-ve-b-olasiligi\/","title":{"rendered":"A ve b&#39;nin olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur: \u00f6rneklerle"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">A ve B olmak \u00fczere iki olay verildi\u011finde, &#8220;A ve B&#8217;nin olas\u0131l\u0131\u011f\u0131n\u0131 bulmak&#8221; <strong>, A olay\u0131n\u0131n ve B olay\u0131n\u0131n her ikisinin de meydana gelme<\/strong> olas\u0131l\u0131\u011f\u0131n\u0131 bulmak anlam\u0131na gelir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu olas\u0131l\u0131\u011f\u0131 genellikle iki \u015fekilde yazar\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A ve B) \u2013 Yaz\u0131l\u0131 form<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u2229B) \u2013 Form g\u00f6sterimi<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu olas\u0131l\u0131\u011f\u0131 nas\u0131l hesaplad\u0131\u011f\u0131m\u0131z A ve B olaylar\u0131n\u0131n ba\u011f\u0131ms\u0131z veya ba\u011f\u0131ml\u0131 olmas\u0131na ba\u011fl\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A ve B <strong>ba\u011f\u0131ms\u0131zsa<\/strong> P(A\u2229B)&#8217;yi hesaplamak i\u00e7in kulland\u0131\u011f\u0131m\u0131z form\u00fcl basit\u00e7e \u015f\u00f6yledir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 19px;\"> <strong><span style=\"color: #000000;\">Independent Events:<\/span> <span style=\"color: #000000;\">P(A\u2229B) = P(A) * P(B)<\/span>\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A ve B <strong>ba\u011f\u0131ml\u0131ysa<\/strong> P(A\u2229B)&#8217;yi hesaplamak i\u00e7in kulland\u0131\u011f\u0131m\u0131z form\u00fcl \u015f\u00f6yledir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 19px;\"> <strong><span style=\"color: #000000;\">Dependent Events:<\/span> <span style=\"color: #000000;\">P(A\u2229B) = P(A) * P(B|A)<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">P(B|A)&#8217;n\u0131n, <em>verilen<\/em> B olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131 oldu\u011funa dikkat edin. <em><strong>&nbsp;<\/strong><\/em> A olay\u0131 ger\u00e7ekle\u015fir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler bu form\u00fcllerin pratikte nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131z olaylar i\u00e7in P(A\u2229B) \u00f6rnekleri<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, A ve B ba\u011f\u0131ms\u0131z olaylar oldu\u011funda P(A\u2229B)&#8217;nin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong> Tuttu\u011funuz beyzbol tak\u0131m\u0131n\u0131n D\u00fcnya Serisini kazanma olas\u0131l\u0131\u011f\u0131 1\/30, tuttu\u011funuz futbol tak\u0131m\u0131n\u0131n Super Bowl&#8217;u kazanma olas\u0131l\u0131\u011f\u0131 ise 1\/32&#8217;dir. Favori iki tak\u0131m\u0131n\u0131z\u0131n kendi \u015fampiyonalar\u0131n\u0131 kazanma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Bu \u00f6rnekte her bir olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 di\u011ferinden ba\u011f\u0131ms\u0131zd\u0131r. Yani her ikisinin de ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u2229B) = (1\/30) * (1\/32) = 1\/960 = 0,00104.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong> Ayn\u0131 anda hem zar at\u0131yorsunuz hem de paray\u0131 at\u0131yorsunuz. Zar\u0131n 4&#8217;e ve paran\u0131n yaz\u0131ya gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Bu \u00f6rnekte her bir olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 di\u011ferinden ba\u011f\u0131ms\u0131zd\u0131r. Yani her ikisinin de ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u2229B) = (1\/6) * (1\/2) = 1\/12 = 0,083333.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ml\u0131 olaylar i\u00e7in P(A\u2229B) \u00f6rnekleri<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, A ve B ba\u011f\u0131ml\u0131 olaylar oldu\u011funda P(A\u2229B)&#8217;nin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong> Bir kavanozda 4 k\u0131rm\u0131z\u0131 ve 4 ye\u015fil top bulunmaktad\u0131r. Tornadan rastgele bir top se\u00e7iyorsunuz. Daha sonra de\u011fi\u015ftirmeden ba\u015fka bir top se\u00e7ersiniz. Her seferinde k\u0131rm\u0131z\u0131 bir top se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131z nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Bu \u00f6rnekte ilk seferde se\u00e7ti\u011finiz topun rengi ikinci seferde k\u0131rm\u0131z\u0131 top se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 etkilemektedir. Bu nedenle iki olay ba\u011f\u0131ml\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131n\u0131 ilk seferde k\u0131rm\u0131z\u0131 topun se\u00e7ilme olas\u0131l\u0131\u011f\u0131 olarak tan\u0131mlayal\u0131m. Bu olas\u0131l\u0131k P(A) = 4\/8&#8217;dir. Daha sonra, ilk topun k\u0131rm\u0131z\u0131 oldu\u011fu <em>g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda<\/em> , tekrar k\u0131rm\u0131z\u0131 topun se\u00e7ilme olas\u0131l\u0131\u011f\u0131n\u0131 bulmam\u0131z gerekiyor. Bu durumda se\u00e7ilebilecek yaln\u0131zca 3 k\u0131rm\u0131z\u0131 top kal\u0131r ve torbada toplamda yaln\u0131zca 7 top kal\u0131r. B\u00f6ylece P(B|A) 3\/7 olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani her seferinde k\u0131rm\u0131z\u0131 top se\u00e7me olas\u0131l\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u2229B) = P(A) * P(B|A) = (4\/8) * (3\/7) = 0,214.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong> Bir s\u0131n\u0131fta 15 erkek ve 12 k\u0131z \u00f6\u011frenci bulunmaktad\u0131r. Her \u00f6\u011frencinin ad\u0131n\u0131 bir torbaya koydu\u011fumuzu varsayal\u0131m. \u00c7antadan rastgele bir isim se\u00e7iyoruz. Daha sonra de\u011fi\u015ftirmeden ba\u015fka bir isim se\u00e7iyoruz. Her iki ismin de erkek olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Bu \u00f6rnekte ilk seferde se\u00e7ti\u011fimiz ilk isim, ikinci \u00e7izimde bir erkek \u00e7ocu\u011funun ilk ismini se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 etkilemektedir. Bu nedenle iki olay ba\u011f\u0131ml\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131n\u0131 ilk kez bir erkek \u00e7ocu\u011fu se\u00e7me olas\u0131l\u0131\u011f\u0131 olarak tan\u0131mlayal\u0131m. Bu olas\u0131l\u0131k P(A) = 15\/27&#8217;dir. Daha sonra, ilk ismin erkek oldu\u011fu <em>g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda<\/em> , tekrar erkek \u00e7ocuk se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 bulmam\u0131z gerekiyor. Bu durumda se\u00e7ilebilecek sadece 14 erkek \u00e7ocuk kal\u0131yor ve \u00e7antada toplamda sadece 26 isim kal\u0131yor. B\u00f6ylece P(B|A) 14\/26 olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yani her seferinde bir erkek \u00e7ocu\u011fun ad\u0131n\u0131 se\u00e7me olas\u0131l\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde hesaplanacakt\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u2229B) = P(A) * P(B|A) = (15\/27) * (14\/26) = 0,299.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A ve B olmak \u00fczere iki olay verildi\u011finde, &#8220;A ve B&#8217;nin olas\u0131l\u0131\u011f\u0131n\u0131 bulmak&#8221; , A olay\u0131n\u0131n ve B olay\u0131n\u0131n her ikisinin de meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 bulmak anlam\u0131na gelir. Bu olas\u0131l\u0131\u011f\u0131 genellikle iki \u015fekilde yazar\u0131z: P(A ve B) \u2013 Yaz\u0131l\u0131 form P(A\u2229B) \u2013 Form g\u00f6sterimi Bu olas\u0131l\u0131\u011f\u0131 nas\u0131l hesaplad\u0131\u011f\u0131m\u0131z A ve B olaylar\u0131n\u0131n ba\u011f\u0131ms\u0131z veya ba\u011f\u0131ml\u0131 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-1343","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>A ve B&#039;nin olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur: \u00f6rneklerle<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, hem A olay\u0131n\u0131n hem de B olay\u0131n\u0131n meydana gelme 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