{"id":400,"date":"2023-08-01T02:01:55","date_gmt":"2023-08-01T02:01:55","guid":{"rendered":"https:\/\/statorials.org\/tr\/olasilik-teorisi\/"},"modified":"2023-08-01T02:01:55","modified_gmt":"2023-08-01T02:01:55","slug":"olasilik-teorisi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olasilik-teorisi\/","title":{"rendered":"Olas\u0131l\u0131k teorisi"},"content":{"rendered":"<p>Bu makalede olas\u0131l\u0131k teorisinin ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olas\u0131l\u0131k teorisinin temel kavramlar\u0131n\u0131n yan\u0131 s\u0131ra olas\u0131l\u0131k teorisinin \u00f6zelliklerini ve yasalar\u0131n\u0131 da bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-teoria-de-la-probabilidad\"><\/span> Olas\u0131l\u0131k teorisi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Olas\u0131l\u0131k teorisi,<\/strong> rastgele bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan bir dizi kural ve \u00f6zelliktir. B\u00f6ylece olas\u0131l\u0131k teorisi, rastgele bir deneyin hangi sonucunun ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131n\u0131n en y\u00fcksek oldu\u011funu bilmemize olanak tan\u0131r.<\/p>\n<p> Rastgele bir olay\u0131n, sonucu tahmin edilemeyen ancak \u015fansa ba\u011fl\u0131 olan bir deneyden elde edilebilecek bir sonu\u00e7 oldu\u011funu unutmay\u0131n. Dolay\u0131s\u0131yla olas\u0131l\u0131k teorisi, rastgele bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirlememize olanak tan\u0131yan bir dizi yasad\u0131r.<\/p>\n<p> \u00d6rne\u011fin, bir paray\u0131 att\u0131\u011f\u0131m\u0131zda iki olas\u0131 sonu\u00e7 elde edebiliriz: yaz\u0131 veya tura. Bu durumda %50 olan tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in olas\u0131l\u0131k teorisini kullanabiliriz.<\/p>\n<p> Tarih boyunca olas\u0131l\u0131k teorisinin geli\u015fimine bir\u00e7ok ki\u015fi katk\u0131da bulunmu\u015ftur; bunlar\u0131n aras\u0131nda Cardano, Laplace, Gauss ve Kolmogorov \u00f6ne \u00e7\u0131kmaktad\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\/olasilik-formulleri\/\">Olas\u0131l\u0131k form\u00fclleri<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"conceptos-basicos-de-la-teoria-de-la-probabilidad\"><\/span> Olas\u0131l\u0131k teorisinin temelleri <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"espacio-muestral\"><\/span> \u00d6rnek uzay<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Olas\u0131l\u0131k teorisinde <strong>\u00f6rnek uzay<\/strong> , rastgele bir deneyin t\u00fcm olas\u0131 sonu\u00e7lar\u0131n\u0131n k\u00fcmesidir.<\/p>\n<p> \u00d6rnek uzay\u0131n sembol\u00fc b\u00fcy\u00fck Yunan harfi Omega&#8217;d\u0131r (\u03a9), ancak b\u00fcy\u00fck E harfiyle de temsil edilebilir.<\/p>\n<p> \u00d6rne\u011fin, bir zar\u0131n at\u0131lmas\u0131 i\u00e7in \u00f6rnek uzay: <\/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-b3ad0ac057b6cd7e3d3db78b556249a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Omega=\\{1,2,3,4,5,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\"><\/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\/ornek-uzay-1\/\">\u00d6rnek uzay<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"suceso\"><\/span> Etkinlik<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Olas\u0131l\u0131k teorisinde, bir <strong>olay<\/strong> (veya olu\u015fum), rastgele bir deneyin her olas\u0131 sonucudur. Dolay\u0131s\u0131yla bir olay\u0131n olas\u0131l\u0131\u011f\u0131, bir sonucun ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren bir de\u011ferdir.<\/p>\n<p> \u00d6rne\u011fin, yaz\u0131-tura at\u0131\u015f\u0131nda iki olay vard\u0131r: &#8220;tura&#8221; ve &#8220;yaz\u0131&#8221;.<\/p>\n<p> Farkl\u0131 t\u00fcrde olaylar vard\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Temel olay (veya basit olay):<\/strong> deneyin olas\u0131 sonu\u00e7lar\u0131n\u0131n her biri.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Bile\u015fik olay:<\/strong> Bu, \u00f6rnek uzay\u0131n bir alt k\u00fcmesidir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Kesin Olay:<\/strong> Bu her zaman meydana gelecek rastgele bir deneyimin sonucudur.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0130mkans\u0131z Olay:<\/strong> Bu hi\u00e7bir zaman ger\u00e7ekle\u015fmeyecek rastgele bir deneyin sonucudur.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Uyumlu olaylar:<\/strong> Ortak bir temel olaya sahip olan iki olay uyumludur.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Uyumsuz olaylar:<\/strong> Herhangi bir temel olay\u0131 payla\u015fmayan iki olay uyumsuzdur.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ba\u011f\u0131ms\u0131z Olaylar:<\/strong> Birinin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 di\u011ferinin olas\u0131l\u0131\u011f\u0131n\u0131 etkilemiyorsa iki olay ba\u011f\u0131ms\u0131zd\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ba\u011f\u0131ml\u0131 olaylar:<\/strong> \u0130ki olaydan birinin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 di\u011ferinin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 de\u011fi\u015ftiriyorsa bu olaylar ba\u011f\u0131ml\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Birbirine ayk\u0131r\u0131 olay:<\/strong> Di\u011fer olay meydana gelmedi\u011finde meydana gelen olay.<\/span> <\/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> Etkinlik t\u00fcrleri <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"axiomas-de-la-probabilidad\"><\/span> Olas\u0131l\u0131k aksiyomlar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k aksiyomlar\u0131 \u015funlard\u0131r:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Olas\u0131l\u0131k Aksiyomu 1<\/strong> : Bir olay\u0131n olas\u0131l\u0131\u011f\u0131 negatif olamaz.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-60e0ca200964690b247a4dd29a7533ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0\\leq P(A)\\leq 1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Olas\u0131l\u0131k Aksiyomu 2<\/strong> : Belirli bir olay\u0131n olas\u0131l\u0131\u011f\u0131 1&#8217;dir.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3bce9a4bd2e6e64bfb5c0563de6106a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\Omega)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Olas\u0131l\u0131k Aksiyomu 3<\/strong> : Bir dizi uyumsuz olay\u0131n olas\u0131l\u0131\u011f\u0131, t\u00fcm olas\u0131l\u0131klar\u0131n toplam\u0131na e\u015fittir.<\/span> <\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fe646d340e4b18901999affd42bbaa21_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cap B= \\varnothing \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ P(A\\cup B)=P(A)+P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"422\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/ol>\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\/olasilik-aksiyomlari\/\">Olas\u0131l\u0131k aksiyomlar\u0131<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-la-probabilidad\"><\/span> Olas\u0131l\u0131k \u00d6zellikleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k \u00f6zellikleri \u015funlard\u0131r:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Bir olay\u0131n olas\u0131l\u0131\u011f\u0131, bir eksi kar\u015f\u0131t olay\u0131n olas\u0131l\u0131\u011f\u0131na e\u015fittir.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e0d62ccd1f8f95072d222f71dc749d90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\\bigl(A\\bigr)=1-P\\bigl(\\overline{A}\\bigr)\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"139\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0130mkans\u0131z bir olay\u0131n olas\u0131l\u0131\u011f\u0131 her zaman s\u0131f\u0131rd\u0131r.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8a100ef3cff594784306812f09ec1edf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\varnothing)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Bir olay\u0131n ba\u015fka bir olaya dahil olmas\u0131 durumunda, ilk olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n ikinci olay\u0131n olas\u0131l\u0131\u011f\u0131ndan k\u00fc\u00e7\u00fck veya ona e\u015fit olmas\u0131 gerekir.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-305a2b392adf58d4a453451588cc8df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\subset B \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ P(A)\\leq P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"292\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0130ki olay\u0131n birle\u015fme olas\u0131l\u0131\u011f\u0131, her bir olay\u0131n ayr\u0131 ayr\u0131 meydana gelme olas\u0131l\u0131\u011f\u0131 ile bunlar\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n toplam\u0131na e\u015fittir.<\/span><\/li>\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<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u0130kiye iki uyumsuz olaylar dizisi verildi\u011finde, bunlar\u0131n ortak olas\u0131l\u0131klar\u0131, her bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 eklenerek hesaplan\u0131r.<\/span><\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-764b23b74452aaa9dae225ca858b6621_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_1\\cup A_2 \\cup \\ldots\\cup A_n)=P(A_1)+P(A_2)+\\ldots+P(A_n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"428\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Bir \u00f6rnek uzaydaki t\u00fcm temel olaylar\u0131n olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131 1&#8217;e e\u015fittir.<\/span> <\/li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-191a5226cbed021795400db02c08ed57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Omega=\\{A_1,A_2,\\ldots,A_n\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" 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-ee0f59a00301b4e664c0c7b9d36de757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A_1)+P(A_2)+\\ldots+P(A_n)=1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"265\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<\/ol>\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\/olasilik-ozellikleri\/\">Olas\u0131l\u0131\u011f\u0131n \u00f6zellikleri<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"reglas-de-la-probabilidad\"><\/span> Olas\u0131l\u0131k kurallar\u0131 <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-laplace\"><\/span> Laplace kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Laplace kural\u0131,<\/strong> bir \u00f6rnek uzayda meydana gelen bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan olas\u0131l\u0131ksal bir kurald\u0131r.<\/p>\n<p> Daha spesifik olarak Laplace kural\u0131, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n, olumlu durumlar\u0131n say\u0131s\u0131n\u0131n toplam olas\u0131 durum say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fit oldu\u011funu s\u00f6yl\u00fcyor. Laplace kural\u0131n\u0131n form\u00fcl\u00fc bu nedenle 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-d3b5a3fd8897ec1933cfc654566b84dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{\\text{casos favorables}}{\\text{casos posibles}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"190\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> \u00d6rne\u011fin bir torbaya 5 ye\u015fil top, 4 mavi top ve 2 sar\u0131 top koyarsak Laplace kural\u0131n\u0131 kullanarak rastgele bir ye\u015fil top \u00e7ekme olas\u0131l\u0131\u011f\u0131n\u0131 bulabiliriz: <\/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-68f6b4223a63448cf4e89485ee0ca28e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola verde})=\\cfrac{5}{5+4+2}=0,45\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"261\" style=\"vertical-align: -14px;\"><\/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\/laplace-kurali-veya-laplace-yasasi\/\">Laplace kural\u0131 (olas\u0131l\u0131k)<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-suma\"><\/span> toplam kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Olas\u0131l\u0131k teorisinde <strong>toplam kural\u0131<\/strong> (veya toplama kural\u0131), 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 s\u00f6yler. zaman. .<\/p>\n<p> Yani toplama kural\u0131n\u0131n form\u00fcl\u00fc 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> Toplama kural\u0131n\u0131n uygulanmas\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f ad\u0131m ad\u0131m al\u0131\u015ft\u0131rmalar\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\">Toplama kural\u0131 (olas\u0131l\u0131k)<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-multiplicacion\"><\/span> \u00e7arpma kural\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u00c7arpma kural\u0131 (veya \u00e7arp\u0131m kural\u0131),<\/strong> iki ba\u011f\u0131ms\u0131z 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<p> \u00c7arpma kural\u0131n\u0131n form\u00fcl\u00fc bu nedenle 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-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> Ancak \u00e7arpma kural\u0131n\u0131n form\u00fcl\u00fc olaylar\u0131n ba\u011f\u0131ms\u0131z veya ba\u011f\u0131ml\u0131 olmas\u0131na g\u00f6re de\u011fi\u015fir. Ba\u011f\u0131ml\u0131 olaylar i\u00e7in \u00e7arpma kural\u0131 form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve bu kural\u0131n uygulama \u00f6rneklerini buraya t\u0131klayarak 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\/carpma-kurali\/\">\u00c7arpma kural\u0131 (olas\u0131l\u0131k)<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede olas\u0131l\u0131k teorisinin ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olas\u0131l\u0131k teorisinin temel kavramlar\u0131n\u0131n yan\u0131 s\u0131ra olas\u0131l\u0131k teorisinin \u00f6zelliklerini ve yasalar\u0131n\u0131 da bulacaks\u0131n\u0131z. Olas\u0131l\u0131k teorisi nedir? Olas\u0131l\u0131k teorisi, rastgele bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lan bir dizi kural ve \u00f6zelliktir. B\u00f6ylece olas\u0131l\u0131k teorisi, rastgele bir deneyin hangi sonucunun ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131n\u0131n en y\u00fcksek [&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-400","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 Olas\u0131l\u0131k teorisi<\/title>\n<meta name=\"description\" content=\"Burada olas\u0131l\u0131k teorisinin ne oldu\u011funu, olas\u0131l\u0131k teorisi kavramlar\u0131n\u0131, olas\u0131l\u0131\u011f\u0131n \u00f6zelliklerini ve kurallar\u0131n\u0131 \u00f6\u011freneceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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