{"id":365,"date":"2023-08-01T19:09:16","date_gmt":"2023-08-01T19:09:16","guid":{"rendered":"https:\/\/statorials.org\/tr\/carpma-kurali\/"},"modified":"2023-08-01T19:09:16","modified_gmt":"2023-08-01T19:09:16","slug":"carpma-kurali","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/carpma-kurali\/","title":{"rendered":"\u00c7arpma kural\u0131"},"content":{"rendered":"<p>Bu makale olas\u0131l\u0131k teorisinde \u00e7arp\u0131m kural\u0131 olarak da adland\u0131r\u0131lan \u00e7arpma kural\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece \u00e7arpma kural\u0131n\u0131n form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, \u00e7arpma kural\u0131n\u0131 kullanarak bir olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair \u00f6rnekleri ve ek olarak uygulayabilece\u011finiz \u00e7e\u015fitli \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 bulacaks\u0131n\u0131z.<\/p>\n<p> \u00c7arpma kural\u0131 olaylar\u0131n ba\u011f\u0131ms\u0131z ya da ba\u011f\u0131ml\u0131 olmas\u0131na ba\u011fl\u0131d\u0131r; bu nedenle \u00f6nce ba\u011f\u0131ms\u0131z olaylar i\u00e7in, sonra da ba\u011f\u0131ml\u0131 olaylar i\u00e7in kural\u0131n nas\u0131l g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc g\u00f6rece\u011fiz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-multiplicacion-para-eventos-independientes\"><\/span> Ba\u011f\u0131ms\u0131z olaylar i\u00e7in \u00e7arpma kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ba\u011f\u0131ms\u0131z olaylar\u0131n, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olmayan istatistiksel bir deneyin sonu\u00e7lar\u0131 oldu\u011funu unutmay\u0131n. Ba\u015fka bir deyi\u015fle, A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 B olay\u0131n\u0131n meydana gelmesine ba\u011fl\u0131 de\u011filse A ve B olaylar\u0131 ba\u011f\u0131ms\u0131zd\u0131r ve bunun tersi de ge\u00e7erlidir. <\/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 nelerdir?<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-regla-de-la-multiplicacion-para-eventos-independientes\"><\/span> Ba\u011f\u0131ms\u0131z olaylar i\u00e7in \u00e7arpma kural\u0131 form\u00fcl\u00fc <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> \u0130ki olay ba\u011f\u0131ms\u0131z oldu\u011funda <strong>\u00e7arpma kural\u0131<\/strong> , her iki olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n her bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fit oldu\u011funu s\u00f6yler.<\/p>\n<\/div>\n<p> Bu nedenle ba\u011f\u0131ms\u0131z olaylar i\u00e7in \u00e7arpma kural\u0131n\u0131n form\u00fcl\u00fc \u015f\u00f6yledir:<\/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 ve B olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ortak olas\u0131l\u0131kt\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\/bilesik-olasilik\/\">Ortak olas\u0131l\u0131k nedir?<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-de-la-multiplicacion-para-eventos-independientes\"><\/span> Ba\u011f\u0131ms\u0131z olaylar i\u00e7in \u00f6rnek \u00e7arpma kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Bir madeni para art arda \u00fc\u00e7 kez at\u0131l\u0131yor. \u00dc\u00e7 at\u0131\u015fta da tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplay\u0131n.<\/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\u015f\u0131k \u00fc\u00e7 tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in ba\u011f\u0131ms\u0131z olaylar i\u00e7in \u00e7arpma kural\u0131 form\u00fcl\u00fcn\u00fc kullanmam\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-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> Yaz\u0131 tura att\u0131\u011f\u0131m\u0131zda sadece iki olas\u0131 sonu\u00e7 vard\u0131r; yaz\u0131 veya tura gelebiliriz. 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 class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1bc45ea1827985f95c0e3199c9bc2bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cruz})=\\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-e107223e0e6a05a2bfaaf05dcc8d33a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara}\\cap \\text{cara}\\cap \\text{cara})=0,5\\cdot 0,5\\cdot 0,5=0,125\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"357\" style=\"vertical-align: -5px;\"><\/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<p> A\u015fa\u011f\u0131da olas\u0131l\u0131klar\u0131yla birlikte bir a\u011fa\u00e7 diyagram\u0131nda temsil edilen t\u00fcm olas\u0131 olaylar\u0131 g\u00f6r\u00fcyorsunuz, bu \u015fekilde ortak olas\u0131l\u0131\u011f\u0131 elde etmek i\u00e7in takip etti\u011fimiz s\u00fcreci daha iyi g\u00f6rebilirsiniz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/diagramme-arborescent-calcul-de-probabilite.png\" alt=\"\" class=\"wp-image-3135\" width=\"436\" height=\"364\" srcset=\"\" sizes=\"auto, \"><\/figure>\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\/agac-diyagrami\/\">A\u011fa\u00e7 diyagram\u0131 nedir?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-multiplicacion-para-eventos-dependientes\"><\/span> Ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00e7arpma kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k ba\u011f\u0131ms\u0131z olaylar i\u00e7in \u00e7arpma kural\u0131n\u0131n ne oldu\u011funu g\u00f6rd\u00fc\u011f\u00fcm\u00fcze g\u00f6re, form\u00fcl biraz farkl\u0131l\u0131k g\u00f6sterdi\u011fi i\u00e7in bu yasan\u0131n ba\u011f\u0131ml\u0131 olaylar i\u00e7in nas\u0131l g\u00f6r\u00fcnd\u00fc\u011f\u00fcne bakal\u0131m.<\/p>\n<p> Ba\u011f\u0131ml\u0131 olaylar\u0131n, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olan rastgele bir deneyin sonu\u00e7lar\u0131 oldu\u011funu unutmay\u0131n. 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<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\/olaylara-bagli-olaylar\/\">Ba\u011f\u0131ml\u0131 olaylar nelerdir?<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-regla-de-la-multiplicacion-para-eventos-dependientes\"><\/span> Ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00e7arpma kural\u0131 form\u00fcl\u00fc <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> \u0130ki olay ba\u011f\u0131ml\u0131 oldu\u011funda <strong>\u00e7arpma kural\u0131<\/strong> , her iki olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n, ilk olay g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda di\u011fer olay\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131 ile \u00e7arp\u0131m\u0131na e\u015fit oldu\u011funu s\u00f6yler.<\/p>\n<\/div>\n<p> Yani ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00e7arpma kural\u0131n\u0131n form\u00fcl\u00fc \u015f\u00f6yledir:<\/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 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\u0131n\u0131n ve 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-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<\/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 nedir?<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-de-la-multiplicacion-para-eventos-dependientes\"><\/span> Ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00f6rnek \u00e7arpma kural\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 ortak olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00e7arpma kural\u0131 form\u00fcl\u00fcn\u00fc kullanmam\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-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 bir top \u00e7ekmenin ortak 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\">Toplama kural\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-regla-de-la-multiplicacion\"><\/span> \u00c7arpma kural\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> 1. Egzersiz<\/h3>\n<p> Bir il\u00e7ede sadece 3 kre\u015f bulunmaktad\u0131r: \u00c7ocuklar\u0131n %60&#8217;\u0131 A kre\u015fine, %30&#8217;u B kre\u015fine ve %10&#8217;u C kre\u015fine gitmektedir. Ayr\u0131ca \u00fc\u00e7 kre\u015fte n\u00fcfusun %55&#8217;i k\u0131zd\u0131r. A\u015fa\u011f\u0131daki olas\u0131l\u0131klar\u0131 hesaplay\u0131n:<\/p>\n<ul>\n<li> B kre\u015finden rastgele se\u00e7ilen bir \u00e7ocu\u011fun k\u0131z olma olas\u0131l\u0131\u011f\u0131.<\/li>\n<li> Herhangi bir kre\u015ften rastgele se\u00e7ilen bir \u00e7ocu\u011fun erkek olma olas\u0131l\u0131\u011f\u0131. <\/li>\n<\/ul>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> T\u00fcm kre\u015flerdeki k\u0131z \u00e7ocuklar\u0131n oran\u0131 %55 ise, erkek \u00e7ocuklar\u0131n y\u00fczdesi basit\u00e7e 1 eksi 0,55 \u00e7\u0131kar\u0131larak 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-d6c48cfc81fd4e8283d9366bced38a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico})=1-0,55=0,45\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Art\u0131k t\u00fcm olas\u0131l\u0131klar\u0131 bildi\u011fimize g\u00f6re, t\u00fcm olas\u0131l\u0131klar\u0131n olas\u0131l\u0131klar\u0131n\u0131 i\u00e7eren bir a\u011fa\u00e7 olu\u015fturabiliriz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exercice-resolu-du-diagramme-arborescent.png\" alt=\"a\u011fa\u00e7 egzersizi \u00e7\u00f6z\u00fcld\u00fc\" class=\"wp-image-3140\" width=\"312\" height=\"330\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p class=\"has-text-align-left\"> Bu durumda, k\u0131z ya da erkek olma olas\u0131l\u0131\u011f\u0131 se\u00e7ilen kre\u015fe ba\u011fl\u0131 olmad\u0131\u011f\u0131ndan olaylar ba\u011f\u0131ms\u0131zd\u0131r. Dolay\u0131s\u0131yla, kre\u015f B&#8217;den rastgele bir k\u0131z se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in, kre\u015f B&#8217;yi se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 bir k\u0131z se\u00e7me olas\u0131l\u0131\u011f\u0131yla \u00e7arpman\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-8da69823ee95f9d3eb866b8830c69459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chica guarder\\'ia B})=0,30\\cdot 0,55=\\bm{0,165}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u00d6te yandan, herhangi bir kre\u015fe erkek \u00e7ocuk se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in \u00f6nce her kre\u015fe bir erkek \u00e7ocuk se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamal\u0131, sonra bunlar\u0131 toplamal\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-cba123bdad65bc0ef13fe011d12c16e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia A})=0,6\\cdot 0,45=0,27\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"320\" style=\"vertical-align: -5px;\"><\/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-502aba9717f579b47d3aae94af910f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia B})=0,30\\cdot 0,45=0,135\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" style=\"vertical-align: -5px;\"><\/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-4ab8a01b04f94bda577564f835167d88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia C})=0,10\\cdot 0,45=0,045\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" style=\"vertical-align: -5px;\"><\/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-f2e92f117cfeb16530b9f37c647fe4f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia A, B o C})=0,27+0,135+0,045=\\bm{0,45}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Al\u0131\u015ft\u0131rma 2<\/h3>\n<p> Bir \u00fclkedeki 25 \u015firketin mali y\u0131l\u0131 incelendi ve hisse senedi fiyatlar\u0131n\u0131n o y\u0131l\u0131n ekonomik sonu\u00e7lar\u0131na g\u00f6re nas\u0131l de\u011fi\u015fti\u011fi incelendi. Toplanan verileri a\u015fa\u011f\u0131daki acil durum tablosunda g\u00f6rebilirsiniz: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exercice-de-probabilite-conditionnelle-resolu.png\" alt=\"ko\u015fullu olas\u0131l\u0131k al\u0131\u015ft\u0131rmas\u0131 \u00e7\u00f6z\u00fcld\u00fc\" class=\"wp-image-667\" width=\"344\" height=\"151\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Bir \u015firketin kar elde etmesi ve ayn\u0131 zamanda hisse senedi fiyatlar\u0131n\u0131n y\u00fckselmesi ihtimali ne kadard\u0131r? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Bu durumda olaylar ba\u011f\u0131ml\u0131d\u0131r \u00e7\u00fcnk\u00fc hisse senetlerinin yukar\u0131 veya a\u015fa\u011f\u0131 gitme olas\u0131l\u0131\u011f\u0131 ekonomik sonuca ba\u011fl\u0131d\u0131r. Bu nedenle ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00e7arpma kural\u0131 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-4a2782612358c488cafb90c8c642eb5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{beneficio}\\cap\\text{precio sube})}=P(\\text{beneficio})\\cdot P(\\text{precio sube}|\\text{beneficio})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"520\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Bu nedenle \u00f6ncelikle bir \u015firketin kar elde etme olas\u0131l\u0131\u011f\u0131n\u0131, ikinci olarak da \u015firketin ekonomik kar elde etti\u011finde hisselerinin artma 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-fe323f1e5e9f9e0e8fc44e886a63b476_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{beneficio})=\\cfrac{14}{25}=0,56\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"197\" style=\"vertical-align: -12px;\"><\/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-9a16170cf4dd1928934f317f29631dfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{precio sube}|\\text{beneficio})=\\cfrac{10}{14}=0,71 \" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"288\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Daha sonra hesaplanan de\u011ferleri form\u00fclde yerine koyar\u0131z ve ortak olas\u0131l\u0131\u011f\u0131 hesaplar\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-9ef9a2ba07b99febef46f59960dc628d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(\\text{beneficio}\\cap\\text{precio sube})}=\\\\[2ex]=P(\\text{beneficio})\\cdot P(\\text{precio sube}|\\text{beneficio})=\\\\[2ex]= 0,56\\cdot 0,71=\\\\[2ex] =\\bm{0,4} \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"130\" width=\"332\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale olas\u0131l\u0131k teorisinde \u00e7arp\u0131m kural\u0131 olarak da adland\u0131r\u0131lan \u00e7arpma kural\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece \u00e7arpma kural\u0131n\u0131n form\u00fcl\u00fcn\u00fcn ne oldu\u011funu, \u00e7arpma kural\u0131n\u0131 kullanarak bir olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair \u00f6rnekleri ve ek olarak uygulayabilece\u011finiz \u00e7e\u015fitli \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 bulacaks\u0131n\u0131z. \u00c7arpma kural\u0131 olaylar\u0131n ba\u011f\u0131ms\u0131z ya da ba\u011f\u0131ml\u0131 olmas\u0131na ba\u011fl\u0131d\u0131r; bu nedenle \u00f6nce ba\u011f\u0131ms\u0131z olaylar i\u00e7in, sonra da 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":[12],"tags":[],"class_list":["post-365","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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