{"id":370,"date":"2023-08-01T16:43:21","date_gmt":"2023-08-01T16:43:21","guid":{"rendered":"https:\/\/statorials.org\/tr\/toplama-kurali-veya-toplama-kurali\/"},"modified":"2023-08-01T16:43:21","modified_gmt":"2023-08-01T16:43:21","slug":"toplama-kurali-veya-toplama-kurali","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/toplama-kurali-veya-toplama-kurali\/","title":{"rendered":"Toplama kural\u0131 (veya ekleme kural\u0131)"},"content":{"rendered":"<p>Bu makalede, toplama kural\u0131 olarak da bilinen toplama kural\u0131n\u0131n ne oldu\u011fu, olas\u0131l\u0131k ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayr\u0131ca toplama kural\u0131 form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve bu form\u00fcl\u00fcn nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6steren \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regla-de-la-suma-o-regla-de-la-adicion\"><\/span> Toplama kural\u0131 (veya toplama kural\u0131) nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Toplama kural\u0131<\/strong> (veya <strong>toplama kural\u0131<\/strong> ), iki olay\u0131n olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131n\u0131n, her bir olay\u0131n ayr\u0131 ayr\u0131 meydana gelme olas\u0131l\u0131\u011f\u0131 eksi her iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131 toplam\u0131na e\u015fit oldu\u011funu belirtir.<\/p>\n<p> Bu nedenle toplama kural\u0131n\u0131n form\u00fcl\u00fc P(A\u22c3B)=P(A)+P(B)\u2212P(A\u22c2B) \u015feklindedir.<\/p>\n<p> Bu nedenle, iki olas\u0131l\u0131\u011f\u0131 toplamak i\u00e7in her olas\u0131l\u0131\u011f\u0131 basit\u00e7e ekleyemeyiz, \u00e7\u00fcnk\u00fc iki olay\u0131n ortak olas\u0131l\u0131\u011f\u0131n\u0131 temsil eden terimi de \u00e7\u0131karmam\u0131z gerekir. Ancak baz\u0131 durumlarda, yaln\u0131zca her olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 toplayarak olas\u0131l\u0131klar\u0131n toplam\u0131n\u0131n do\u011fru sonucunu elde edebiliriz. A\u015fa\u011f\u0131da bu durumlar\u0131n ne oldu\u011funu g\u00f6rece\u011fiz.<\/p>\n<p> K\u0131saca toplama kural\u0131, bir olay\u0131n veya di\u011ferinin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131, yani iki olas\u0131 olaydan en az birinin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-regla-de-la-suma\"><\/span> Toplama kural\u0131 form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Toplama kural\u0131, A olay\u0131n\u0131n veya B olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in, A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 art\u0131 B olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 toplamam\u0131z ve her iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 \u00e7\u0131karmam\u0131z gerekti\u011fini s\u00f6yler. .<\/p>\n<p> <strong>Toplama kural\u0131n\u0131n (veya toplama kural\u0131n\u0131n) form\u00fcl\u00fc<\/strong> bu nedenle a\u015fa\u011f\u0131daki gibidir: <\/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\/regle-daddition-ou-regle-daddition.png\" alt=\"toplama kural\u0131 form\u00fcl\u00fc, toplama kural\u0131 form\u00fcl\u00fc\" class=\"wp-image-8422\" width=\"415\" height=\"366\" srcset=\"\" sizes=\"auto, \"><\/figure>\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-e79827dee6ad7d53b96b5497d617f7c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cup B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<p> A olay\u0131n\u0131n veya B olay\u0131n\u0131n 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<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<\/ul>\n<p> Bu nedenle toplam kural\u0131n\u0131 kullanabilmek i\u00e7in iki olay\u0131n ortak olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 bilmeniz gerekir. Bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 a\u015fa\u011f\u0131daki ba\u011flant\u0131da g\u00f6rebilirsiniz: <\/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\/bilesik-olasilik\/\">Ortak olas\u0131l\u0131k nas\u0131l hesaplan\u0131r?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-de-la-suma-para-eventos-excluyentes\"><\/span> \u00d6zel etkinlikler i\u00e7in \u00f6rnek toplam kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Konsepti anlamay\u0131 tamamlamak i\u00e7in toplama kural\u0131n\u0131n nas\u0131l uygulanaca\u011f\u0131na ili\u015fkin bir \u00f6rnek g\u00f6relim.<\/p>\n<ul>\n<li> Bir kutuya 10 mavi top, 6 turuncu top ve 4 ye\u015fil top koyuyoruz. Mavi veya turuncu bir top \u00e7ekme olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Al\u0131\u015ft\u0131rma bizden \u015fu veya bu olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirlememizi ister. Bu nedenle sorunu \u00e7\u00f6zmek i\u00e7in toplama 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-be7c6347c0f331eeb6540ac9e15081dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cup B)=P(A)+P(B)-P(A\\cap B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"299\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Bu nedenle, \u00f6ncelikle <a href=\"https:\/\/statorials.org\/tr\/laplace-kurali-veya-laplace-yasasi\/\">Laplace kural\u0131n\u0131<\/a> kullanarak her bir olay\u0131n ayr\u0131 ayr\u0131 meydana gelme 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-9b1a5b8249e01fe618b08ea0079e1146_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola azul})=\\cfrac{10}{10+6+4}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"251\" style=\"vertical-align: -14px;\"><\/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-a6220946609d47abd9f3fe7cd85d4b14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola naranja})=\\cfrac{6}{10+6+4}=0,3\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"279\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Ancak bu durumda olaylar\u0131n her ikisi de ayn\u0131 anda ger\u00e7ekle\u015femez \u00e7\u00fcnk\u00fc bunlar <a href=\"https:\/\/statorials.org\/tr\/birbirini-dislayan-olaylar\/\">birbirini d\u0131\u015flayan iki olayd\u0131r<\/a> . Yani e\u011fer mavi bir top \u00e7ekersek art\u0131k turuncu bir top \u00e7ekemeyiz ve bunun tersi de ge\u00e7erlidir.<\/p>\n<p> Bu nedenle, her iki olay\u0131n ortak olas\u0131l\u0131\u011f\u0131 s\u0131f\u0131rd\u0131r ve dolay\u0131s\u0131yla toplam kural\u0131 form\u00fcl\u00fc basitle\u015ftirilmi\u015ftir:<\/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-e00a6d1c1398bf9e15fd02b1d93a0354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cup B)=P(A)+P(B)-\\cancelto{0}{P(A\\cap B)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Yani mavi bir top veya turuncu bir top yakalama olas\u0131l\u0131\u011f\u0131n\u0131n hesaplanmas\u0131 \u015fu \u015fekildedir:<\/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-1776904c975b28dbbd57e37f714182ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{bola azul}\\cup \\text{bola naranja})&amp;=P(\\text{bola azul})+P(\\text{bola azul})\\\\[2ex]&amp;=0,5+0,3\\\\[2ex]&amp;=0,8\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"456\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> K\u0131saca kutudan mavi veya turuncu bir top \u00e7ekme olas\u0131l\u0131\u011f\u0131 %80&#8217;dir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-regla-de-la-suma-para-eventos-no-excluyentes\"><\/span>\u00d6zel olmayan etkinlikler i\u00e7in \u00f6rnek ekleme kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olaylar \u00f6zel oldu\u011funda toplama kural\u0131n\u0131n somut bir \u00f6rne\u011fini g\u00f6rd\u00fckten sonra, \u015fimdi olaylar \u00f6zel olmad\u0131\u011f\u0131nda bu yasan\u0131n nas\u0131l kullan\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> Bir paray\u0131 iki kez atarsak en az bir at\u0131\u015fta tura gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Bu durumda olaylar birbirini d\u0131\u015flamaz \u00e7\u00fcnk\u00fc ilk at\u0131\u015fta tura, ikinci at\u0131\u015fta ise yaz\u0131 gelebilir. Toplama kural\u0131n\u0131n form\u00fcl\u00fc bu nedenle basitle\u015ftirilmemi\u015ftir ve 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-be7c6347c0f331eeb6540ac9e15081dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cup B)=P(A)+P(B)-P(A\\cap B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"299\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Bu nedenle, \u00f6ncelikle Laplace kural\u0131n\u0131 uygulayarak yaz\u0131 tura at\u0131ld\u0131\u011f\u0131nda &#8220;tura&#8221; gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamam\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-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> Ek olarak, iki olay ba\u011f\u0131ms\u0131zd\u0131r, dolay\u0131s\u0131yla iki olay\u0131n ortak olas\u0131l\u0131\u011f\u0131n\u0131 <a href=\"https:\/\/statorials.org\/tr\/carpma-kurali\/\">\u00e7arp\u0131m kural\u0131n\u0131<\/a> kullanarak hesaplayabiliriz:<\/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-c1382d107f7e0e3e2f936db296f550df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara}\\cap \\text{cara})=\\cfrac{1}{2}\\cdot \\cfrac{1}{2}=0,5\\cdot 0,5=0,25\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"316\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Son olarak, iki at\u0131\u015ftan en az birinde tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in, de\u011ferleri toplama kural\u0131 form\u00fcl\u00fcnde yerine koyman\u0131z ve hesaplamay\u0131 yapman\u0131z 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-bbdfc38f607783282ef9cd0578dfba06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{cara}\\cup \\text{cara})&amp;=P(\\text{cara})+P(\\text{cara})-P(\\text{cara}\\cap \\text{cara})\\\\[2ex]&amp;=0,5+0,5-0,25\\\\[2ex]&amp;=0,75\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"411\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sonu\u00e7 olarak, bir paray\u0131 iki kez att\u0131\u011f\u0131n\u0131zda en az bir kez tura gelme olas\u0131l\u0131\u011f\u0131 %75&#8217;tir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede, toplama kural\u0131 olarak da bilinen toplama kural\u0131n\u0131n ne oldu\u011fu, olas\u0131l\u0131k ve istatistikte ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ayr\u0131ca toplama kural\u0131 form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve bu form\u00fcl\u00fcn nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6steren \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 g\u00f6rebileceksiniz. Toplama kural\u0131 (veya toplama kural\u0131) nedir? Toplama kural\u0131 (veya toplama kural\u0131 ), iki olay\u0131n olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131n\u0131n, her bir olay\u0131n ayr\u0131 ayr\u0131 meydana [&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-370","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 Toplama kural\u0131 (veya ekleme kural\u0131)<\/title>\n<meta name=\"description\" content=\"Burada toplama kural\u0131n\u0131n (veya toplama kural\u0131n\u0131n) ne oldu\u011funu, form\u00fcl\u00fcn\u00fc ve toplama kural\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar\u0131 bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" 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