{"id":381,"date":"2023-08-01T11:17:03","date_gmt":"2023-08-01T11:17:03","guid":{"rendered":"https:\/\/statorials.org\/tr\/olasilik-yasalari\/"},"modified":"2023-08-01T11:17:03","modified_gmt":"2023-08-01T11:17:03","slug":"olasilik-yasalari","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olasilik-yasalari\/","title":{"rendered":"Olas\u0131l\u0131k kanunlar\u0131"},"content":{"rendered":"<p>Bu yaz\u0131da olas\u0131l\u0131k yasalar\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Yani burada, her bir yasan\u0131n ne anlama geldi\u011fini anlamak i\u00e7in ana olas\u0131l\u0131k yasalar\u0131n\u0131n yan\u0131 s\u0131ra her birinin somut \u00f6rneklerini bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuales-son-las-leyes-de-la-probabilidad\"><\/span> Olas\u0131l\u0131k yasalar\u0131 nelerdir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Olas\u0131l\u0131\u011f\u0131n ana yasalar\u0131<\/strong> \u015funlard\u0131r:<\/p>\n<ul>\n<li> <strong>yasay\u0131 tamamlamak<\/strong><\/li>\n<li> <strong>Laplace yasas\u0131<\/strong><\/li>\n<li> <strong>ekleme kanunu<\/strong><\/li>\n<li> <strong>\u00e7arpma kanunu<\/strong><\/li>\n<\/ul>\n<p> A\u015fa\u011f\u0131da her bir olas\u0131l\u0131k yasas\u0131n\u0131n a\u00e7\u0131klamas\u0131n\u0131 ve somut \u00f6rnekleri g\u00f6rebilirsiniz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ley-del-complemento\"><\/span> yasay\u0131 tamamlamak<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> T\u00fcmleyen yasas\u0131, e\u011fer birinin olas\u0131l\u0131\u011f\u0131n\u0131 biliyorsak, bir olay\u0131n di\u011ferine z\u0131t olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamam\u0131z\u0131 sa\u011flar. Daha spesifik olarak, t\u00fcmleyen yasas\u0131, bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n bir eksi kar\u015f\u0131t olay\u0131n olas\u0131l\u0131\u011f\u0131na e\u015fit oldu\u011funu s\u00f6yler.<\/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-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<p> \u00d6rne\u011fin, 5 say\u0131s\u0131n\u0131n gelme olas\u0131l\u0131\u011f\u0131 0,167&#8217;dir, \u00e7\u00fcnk\u00fc t\u00fcmleyen yasas\u0131n\u0131 kullanarak ba\u015fka bir say\u0131n\u0131n gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirleyebiliriz: <\/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-e788117c866c89ae91541e23b4f3c548_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(5)=0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" 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-e3524f2e9cc4c5e46291f12f8eb9cfe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1, 2, 3, 4, 6)=1-P(5)=1-0,167=0,833\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"359\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ley-de-laplace\"><\/span> Laplace yasas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Laplace yasas\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 yasad\u0131r.<\/p>\n<p> Daha spesifik olarak Laplace yasas\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 yasas\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 yasas\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 yasas\u0131<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ley-de-la-suma\"><\/span> ekleme kanunu<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Olas\u0131l\u0131k teorisinde <strong>toplama kanunu<\/strong> (veya toplama kanunu), iki olay\u0131n olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131n\u0131n, her bir olay\u0131n ayr\u0131 ayr\u0131 meydana gelme ihtimalinin toplam\u0131 eksi her iki olay\u0131n ayn\u0131 anda meydana gelme ihtimalinin toplam\u0131na e\u015fit oldu\u011funu s\u00f6yler.<\/p>\n<p> Yani toplama kanununun 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 kanununun 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 kanunu (olas\u0131l\u0131k)<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ley-de-la-multiplicacion\"><\/span> \u00e7arpma kanunu<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u00c7arpma kanunu (veya \u00e7arp\u0131m kanunu),<\/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 yasas\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 kanununun form\u00fcl\u00fc olaylar\u0131n ba\u011f\u0131ms\u0131z ya da ba\u011f\u0131ml\u0131 olmas\u0131na g\u00f6re de\u011fi\u015fir. Ba\u011f\u0131ml\u0131 olaylar\u0131n \u00e7arp\u0131m\u0131 kural\u0131n\u0131n form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve bu yasan\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 Yasas\u0131 (olas\u0131l\u0131k)<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"otras-leyes-de-la-probabilidad\"><\/span> Di\u011fer olas\u0131l\u0131k yasalar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak, belirli <a href=\"https:\/\/statorials.org\/tr\/olasilik-dagilimi-1\/\">olas\u0131l\u0131k da\u011f\u0131l\u0131mlar\u0131n\u0131<\/a> takip eden de\u011fi\u015fkenlerin olas\u0131l\u0131klar\u0131n\u0131 hesaplaman\u0131za olanak tan\u0131yan belirli olas\u0131l\u0131k yasalar\u0131yla ilgili \u00e7e\u015fitli makalelerin ba\u011flant\u0131lar\u0131n\u0131 size b\u0131rak\u0131yoruz:<\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-1\/\">binom kanunu<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/cok-terimli-dagilim-1\/\">\u00e7ok terimli yasa<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/balik-kanunu\/\">Poisson yasas\u0131<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/hipergeometrik-dagilim-1\/\">hipergeometrik yasa<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim\/\">normal hukuk<\/a> <\/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\/istatistiksel-degisken-turleri\/\">\u0130statistiksel de\u011fi\u015fken t\u00fcrleri<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131da olas\u0131l\u0131k yasalar\u0131n\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Yani burada, her bir yasan\u0131n ne anlama geldi\u011fini anlamak i\u00e7in ana olas\u0131l\u0131k yasalar\u0131n\u0131n yan\u0131 s\u0131ra her birinin somut \u00f6rneklerini bulacaks\u0131n\u0131z. Olas\u0131l\u0131k yasalar\u0131 nelerdir? Olas\u0131l\u0131\u011f\u0131n ana yasalar\u0131 \u015funlard\u0131r: yasay\u0131 tamamlamak Laplace yasas\u0131 ekleme kanunu \u00e7arpma kanunu A\u015fa\u011f\u0131da her bir olas\u0131l\u0131k yasas\u0131n\u0131n a\u00e7\u0131klamas\u0131n\u0131 ve somut \u00f6rnekleri g\u00f6rebilirsiniz. yasay\u0131 tamamlamak T\u00fcmleyen [&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-381","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 kanunlar\u0131<\/title>\n<meta name=\"description\" content=\"Burada olas\u0131l\u0131\u011f\u0131n ana yasalar\u0131n\u0131n yan\u0131 s\u0131ra her olas\u0131l\u0131k 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