{"id":1459,"date":"2023-07-26T07:41:17","date_gmt":"2023-07-26T07:41:17","guid":{"rendered":"https:\/\/statorials.org\/tr\/toplam-olasilik-yasasi\/"},"modified":"2023-07-26T07:41:17","modified_gmt":"2023-07-26T07:41:17","slug":"toplam-olasilik-yasasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/toplam-olasilik-yasasi\/","title":{"rendered":"Toplam olas\u0131l\u0131k yasas\u0131: tan\u0131m ve \u00f6rnekler"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Olas\u0131l\u0131k teorisinde, <strong>toplam olas\u0131l\u0131k yasas\u0131,<\/strong> <em>A<\/em> olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 do\u011frudan bilmedi\u011fimizde ancak <em>B<\/em> <sub>1<\/sub> , <em>B<\/em> <sub>2<\/sub> , <em>B<\/em> <sub>3<\/sub> &#8230; olaylar\u0131n\u0131n bir b\u00f6l\u00fcm olu\u015fturdu\u011funu <em>bildi\u011fimizde<\/em> , bir A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 bulman\u0131n yararl\u0131 bir yoludur. <a href=\"https:\/\/statorials.org\/tr\/ornek-uzay-1\/\" target=\"_blank\" rel=\"noopener\">\u00f6rnek uzay\u0131<\/a> <em>S.<\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu yasa a\u015fa\u011f\u0131dakileri belirtir:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>Toplam olas\u0131l\u0131k yasas\u0131<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer <em>B<\/em> <sub>1<\/sub> , <em>B<\/em> <sub>2<\/sub> , <em>B<\/em> <sub>3<\/sub> \u2026 \u00f6rnek uzay <em>S&#8217;nin<\/em> bir b\u00f6l\u00fcm\u00fcn\u00fc olu\u015fturuyorsa, o zaman <em>A<\/em> olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 a\u015fa\u011f\u0131daki gibi hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>Bir<\/em> ) = \u03a3P( <em>A<\/em> | <em>B<\/em> <sub>ben<\/sub> )*P( <em>B<\/em> <sub>ben<\/sub> )<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Bu yasay\u0131 anlaman\u0131n en kolay yolu basit bir \u00f6rnek almakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir kutuda a\u015fa\u011f\u0131daki bilyelerin bulundu\u011fu iki torba oldu\u011funu varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Torba 1:<\/strong> 7 k\u0131rm\u0131z\u0131 bilye ve 3 ye\u015fil bilye<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Torba 2:<\/strong> 2 k\u0131rm\u0131z\u0131 bilye ve 8 ye\u015fil bilye<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Torbalardan birini rastgele se\u00e7ip, o torbadan rastgele bir bilye se\u00e7ersek, bunun ye\u015fil bilye olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu \u00f6rnekte P( <em>G<\/em> ) = ye\u015fil bilyeyi se\u00e7me olas\u0131l\u0131\u011f\u0131 olsun. Bizi ilgilendiren olas\u0131l\u0131kt\u0131r ama do\u011frudan hesaplayamay\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine, <em>B<\/em> <sub>i&#8217;nin<\/sub> <em>S<\/em> \u00f6rnek uzay\u0131n\u0131n bir b\u00f6l\u00fcm\u00fcn\u00fc olu\u015fturdu\u011fu bir <em>B<\/em> olay\u0131 verildi\u011finde, <em>G&#8217;nin<\/em> ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131 kullanmam\u0131z gerekir. Bu \u00f6rnekte, a\u015fa\u011f\u0131daki ko\u015fullu olas\u0131l\u0131klara sahibiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(G| <sub>B1<\/sub> ) = 3\/10 = 0,3<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(G| <sub>B2<\/sub> ) = 8\/10 = 0,8<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Toplam olas\u0131l\u0131k yasas\u0131n\u0131 kullanarak ye\u015fil bilye se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(G) = \u03a3P(G|B <sub>i<\/sub> )*P(B <sub>ben<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(G) = P(G|B <sub>1<\/sub> )*P(B <sub>1<\/sub> ) + P(G|B <sub>2<\/sub> )*P(B <sub>2<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(G) = (0,3)*(0,5) + (0,8)*(0,5)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(G) = <strong>0,55<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Torbalardan birini rastgele se\u00e7ip o torbadan rastgele bir bilye se\u00e7ersek ye\u015fil bilye se\u00e7me olas\u0131l\u0131\u011f\u0131m\u0131z <strong>0,55<\/strong> olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Toplam olas\u0131l\u0131k yasas\u0131na ili\u015fkin anlay\u0131\u015f\u0131n\u0131z\u0131 peki\u015ftirmek i\u00e7in a\u015fa\u011f\u0131daki iki \u00f6rne\u011fi okuyun.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Widget&#8217;lar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A \u015eirketi, bir otomobil at\u00f6lyesine aletlerin %80&#8217;ini sa\u011fl\u0131yor ve aletlerin yaln\u0131zca %1&#8217;i ar\u0131zal\u0131 \u00e7\u0131k\u0131yor. B \u015eirketi, aletlerin geri kalan %20&#8217;sini oto tamirhanesine tedarik ediyor ve aletlerinin %3&#8217;\u00fc ar\u0131zal\u0131 \u00e7\u0131k\u0131yor.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14445 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/loitot1.png\" alt=\"Toplam olas\u0131l\u0131k yasas\u0131 \u00f6rne\u011fi\" width=\"363\" height=\"302\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bir m\u00fc\u015fteri bir araba tamirhanesinden rastgele bir alet sat\u0131n al\u0131rsa, bunun kusurlu olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>D<\/em> ) = bir aletin kusurlu olma olas\u0131l\u0131\u011f\u0131n\u0131 ve <em>P(Bi<\/em> <sub>)<\/sub> aletin \u015firketlerden birinden gelme olas\u0131l\u0131\u011f\u0131n\u0131 kabul edersek, o zaman kusurlu bir aletin sat\u0131n al\u0131nma olas\u0131l\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(D) = \u03a3P(D|B <sub>i<\/sub> )*P(B <sub>ben<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(D) = P(D|B <sub>1<\/sub> )*P(B <sub>1<\/sub> ) + P(D|B <sub>2<\/sub> )*P(B <sub>2<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(D) = (0,01)*(0,80) + (0,03)*(0,20)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(D) = <strong>0,014<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu otomobil ma\u011fazas\u0131ndan rastgele bir alet al\u0131rsak, kusurlu olma olas\u0131l\u0131\u011f\u0131 <strong>0,014&#8217;t\u00fcr<\/strong> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Ormanlar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A Orman\u0131 belirli bir park\u0131n toplam alan\u0131n\u0131n %50&#8217;sini kaplar ve bu ormandaki bitkilerin %20&#8217;si zehirlidir. B Orman\u0131 toplam alan\u0131n %30&#8217;unu kaplar ve i\u00e7erdi\u011fi bitkilerin %40&#8217;\u0131 zehirlidir. Orman C, b\u00f6lgenin kalan %20&#8217;sini kapl\u0131yor ve orada bulunan bitkilerin %70&#8217;i zehirli.<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14447 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/loitot2.png\" alt=\"\" width=\"343\" height=\"263\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Bu parka rastgele girsek ve yerden bir bitki se\u00e7sek, onun zehirli olma ihtimali ne kadard\u0131r?<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>P<\/em> ) = bitkinin zehirli olma olas\u0131l\u0131\u011f\u0131n\u0131 ve <em>P(B <sub>i<\/sub> )<\/em> \u00fc\u00e7 ormandan birine girme olas\u0131l\u0131\u011f\u0131n\u0131 kabul edersek, rastgele se\u00e7ilen bir bitkinin zehirli olma olas\u0131l\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(P) = \u03a3P(P|B <sub>i<\/sub> )*P(B <sub>ben<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(P) = P(P|B <sub>1<\/sub> )*P(B <sub>1<\/sub> ) + P(P|B <sub>2<\/sub> )*P(B <sub>2<\/sub> ) + P(P|B <sub>3<\/sub> )*P(B <sub>3<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(P) = (0,20)*(0,50) + (0,40)*(0,30) + (0,70)*(0,20)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(P) = <strong>0,36<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bir bitkiyi yerden rastgele se\u00e7ersek zehirli olma olas\u0131l\u0131\u011f\u0131 <strong>0,36&#8217;d\u0131r<\/strong> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler olas\u0131l\u0131k konular\u0131yla ilgili ek bilgi sa\u011flar:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-ortalamasi\/\" target=\"_blank\" rel=\"noopener\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131 nas\u0131l bulunur?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/olasilik-dagiliminin-standart-sapmasi\/\" target=\"_blank\" rel=\"noopener\">Olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131n standart sapmas\u0131 nas\u0131l bulunur?<\/a><br \/> Olas\u0131l\u0131k Da\u011f\u0131l\u0131m\u0131 Hesaplay\u0131c\u0131s\u0131<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Olas\u0131l\u0131k teorisinde, toplam olas\u0131l\u0131k yasas\u0131, A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 do\u011frudan bilmedi\u011fimizde ancak B 1 , B 2 , B 3 &#8230; olaylar\u0131n\u0131n bir b\u00f6l\u00fcm olu\u015fturdu\u011funu bildi\u011fimizde , bir A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 bulman\u0131n yararl\u0131 bir yoludur. \u00f6rnek uzay\u0131 S. Bu yasa a\u015fa\u011f\u0131dakileri belirtir: Toplam olas\u0131l\u0131k yasas\u0131 E\u011fer B 1 , B 2 , B 3 \u2026 \u00f6rnek [&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-1459","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>Toplam olas\u0131l\u0131k yasas\u0131: tan\u0131m ve \u00f6rnekler<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, resmi bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere toplam olas\u0131l\u0131k yasas\u0131n\u0131n bir a\u00e7\u0131klamas\u0131 sa\u011flanmaktad\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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