{"id":1344,"date":"2023-07-26T19:17:44","date_gmt":"2023-07-26T19:17:44","guid":{"rendered":"https:\/\/statorials.org\/tr\/a-veya-b-olasiligi\/"},"modified":"2023-07-26T19:17:44","modified_gmt":"2023-07-26T19:17:44","slug":"a-veya-b-olasiligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/a-veya-b-olasiligi\/","title":{"rendered":"A veya b 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 veya B olas\u0131l\u0131\u011f\u0131n\u0131 bulmak&#8221; <strong>, A olay\u0131n\u0131n veya B olay\u0131n\u0131n 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 veya B) \u2013 Yaz\u0131l\u0131 form<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u222aB) \u2013 Bi\u00e7im 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 <a href=\"https:\/\/statorials.org\/tr\/karsilikli-olarak-kapsayici-ve-birbirini-dislayan\/\" target=\"_blank\" rel=\"noopener\">birbirini d\u0131\u015flayan<\/a> olup olmad\u0131\u011f\u0131na ba\u011fl\u0131d\u0131r.<\/span> <span style=\"color: #000000;\">\u0130ki olay ayn\u0131 anda ger\u00e7ekle\u015femiyorsa birbirini d\u0131\u015flayan olaylard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A ve B <strong>birbirini d\u0131\u015fl\u0131yorsa<\/strong> P(A\u222aB)&#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;\">Mutually Exclusive Events:<\/span> <span style=\"color: #000000;\">P(A\u222aB) = P(A) + P(B)<\/span>\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A ve B <strong>birbirini d\u0131\u015flam\u0131yorsa<\/strong> P(A\u222aB)&#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;\">Not Mutually Exclusive Events:<\/span> <span style=\"color: #000000;\">P(A\u222aB) = P(A) + P(B) - P(A\u2229B)<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">P(A\u2229B)&#8217;nin A olay\u0131n\u0131n ve B olay\u0131n\u0131n her ikisinin de meydana gelme olas\u0131l\u0131\u011f\u0131 oldu\u011funa dikkat edin.<\/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>\u00d6rnekler: Birbirini d\u0131\u015flayan olaylar i\u00e7in P(A\u222aB)<\/strong><\/span><\/h3>\n<p> <strong><span style=\"color: #000000;\">\u00d6rnek 1:<\/span><\/strong> <span style=\"color: #000000;\">Bir zar at\u0131ld\u0131\u011f\u0131nda 2 veya 5 gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> A olay\u0131n\u0131 2 at\u0131lmas\u0131 ve B olay\u0131n\u0131 da 5 at\u0131lmas\u0131 olarak tan\u0131mlarsak, bu iki olay birbirini d\u0131\u015flar \u00e7\u00fcnk\u00fc ayn\u0131 anda hem 2 <em>hem de<\/em> 5 atamay\u0131z. Yani 2 veya 5 alma olas\u0131l\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u222aB) = (1\/6) + (1\/6) = 2\/6 = 1\/3.<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">\u00d6rnek 2:<\/span><\/strong> <span style=\"color: #000000;\">Bir kavanozun 3 k\u0131rm\u0131z\u0131 top, 2 ye\u015fil top ve 5 sar\u0131 top i\u00e7erdi\u011fini varsayal\u0131m. Rastgele bir top se\u00e7ti\u011fimizde k\u0131rm\u0131z\u0131 ya da ye\u015fil bir top se\u00e7me olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> A olay\u0131n\u0131 k\u0131rm\u0131z\u0131 top se\u00e7mek ve B olay\u0131n\u0131 ye\u015fil top se\u00e7mek olarak tan\u0131mlarsak, bu iki olay birbirini d\u0131\u015flar \u00e7\u00fcnk\u00fc ayn\u0131 anda hem k\u0131rm\u0131z\u0131 hem de ye\u015fil bir top se\u00e7emeyiz. Yani k\u0131rm\u0131z\u0131 veya ye\u015fil bir top se\u00e7me olas\u0131l\u0131\u011f\u0131m\u0131z \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u222aB) = (3\/10) + (2\/10) = 5\/10 = 1\/2.<\/span><\/p>\n<h3> \u00d6rnekler: <span style=\"color: #000000;\"><strong>Birbirini d\u0131\u015flamayan olaylar i\u00e7in<\/strong><\/span> <span style=\"color: #000000;\"><strong>P(A<\/strong><\/span> <span style=\"color: #000000;\"><strong>\u222a<\/strong><\/span> B)<\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, A ve B birbirini d\u0131\u015flayan olaylar olmad\u0131\u011f\u0131nda P(A\u222aB)&#8217;nin nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong> 52 kartl\u0131k standart bir desteden rastgele bir kart se\u00e7ersek, ma\u00e7a veya k\u0131zdan birini se\u00e7me olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Bu \u00f6rnekte hem Ma\u00e7a <em>hem de<\/em> K\u0131z olan bir kart se\u00e7mek m\u00fcmk\u00fcnd\u00fcr, yani bu iki olay birbirini d\u0131\u015flamaz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131n\u0131 bir ma\u00e7a se\u00e7me olay\u0131 ve B olay\u0131n\u0131 da vezir se\u00e7me olay\u0131 olarak kabul edersek, o zaman a\u015fa\u011f\u0131daki olas\u0131l\u0131klara sahip oluruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A) = 13\/52<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(B) = 4\/52<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u2229B) = 1\/52<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Yani ma\u00e7a ya da vezir se\u00e7me olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u222aB) = P(A) + P(B) \u2013 P(A\u2229B) = (13\/52) + (4\/52) \u2013 (1\/52) = 16\/52 = 4\/13.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong> Bir zar\u0131 atarsak, zar\u0131n 3&#8217;ten b\u00fcy\u00fck bir say\u0131ya veya \u00e7ift say\u0131ya gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> Bu \u00f6rnekte, zar\u0131n hem 3&#8217;ten b\u00fcy\u00fck <em>hem<\/em> de \u00e7ift bir say\u0131ya gelmesi m\u00fcmk\u00fcnd\u00fcr, dolay\u0131s\u0131yla bu iki olay birbirini d\u0131\u015flamaz.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131n\u0131 3&#8217;ten b\u00fcy\u00fck bir say\u0131 alma olay\u0131 ve B olay\u0131n\u0131 da \u00e7ift say\u0131 alma olay\u0131 olarak kabul edersek a\u015fa\u011f\u0131daki olas\u0131l\u0131klara sahip oluruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A) = 3\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(B) = 3\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u2229B) = 2\/6<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">B\u00f6ylece zar\u0131n 3&#8217;ten b\u00fcy\u00fck veya \u00e7ift say\u0131ya gelme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(A\u222aB) = P(A) + P(B) \u2013 P(A\u2229B) = (3\/6) + (3\/6) \u2013 (2\/6) = 4\/6 = 2\/3.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A ve B olmak \u00fczere iki olay verildi\u011finde, &#8220;A veya B olas\u0131l\u0131\u011f\u0131n\u0131 bulmak&#8221; , A olay\u0131n\u0131n veya B olay\u0131n\u0131n 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 veya B) \u2013 Yaz\u0131l\u0131 form P(A\u222aB) \u2013 Bi\u00e7im g\u00f6sterimi Bu olas\u0131l\u0131\u011f\u0131 nas\u0131l hesaplad\u0131\u011f\u0131m\u0131z, A ve B olaylar\u0131n\u0131n birbirini d\u0131\u015flayan olup olmad\u0131\u011f\u0131na ba\u011fl\u0131d\u0131r. \u0130ki [&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-1344","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 veya B olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur: \u00f6rneklerle<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde A veya B 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