{"id":384,"date":"2023-08-01T10:02:49","date_gmt":"2023-08-01T10:02:49","guid":{"rendered":"https:\/\/statorials.org\/tr\/bir-olayin-olasiligi\/"},"modified":"2023-08-01T10:02:49","modified_gmt":"2023-08-01T10:02:49","slug":"bir-olayin-olasiligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/bir-olayin-olasiligi\/","title":{"rendered":"Bir olay\u0131n olas\u0131l\u0131\u011f\u0131"},"content":{"rendered":"<p>Bu makalede bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131, \u00e7\u00f6z\u00fcml\u00fc \u00f6rnekleri ve ayr\u0131ca herhangi bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in \u00e7evrimi\u00e7i bir hesap makinesini bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-de-un-evento\"><\/span> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131 ne kadard\u0131r?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Bir olay\u0131n olas\u0131l\u0131\u011f\u0131,<\/strong> <a href=\"https:\/\/statorials.org\/tr\/istatistiksel-olay\/\">istatistiksel bir olay\u0131n<\/a> meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren bir de\u011ferdir.<\/p>\n<p> Bir olay\u0131n olas\u0131l\u0131k de\u011feri 0 ( <a href=\"https:\/\/statorials.org\/tr\/imkansiz-olay\/\">imkans\u0131z olay<\/a> ) ile 1 ( <a href=\"https:\/\/statorials.org\/tr\/olay-olayi\/\">kesin olay<\/a> ) aras\u0131nda de\u011fi\u015fir, olay\u0131n olas\u0131l\u0131\u011f\u0131 ne kadar y\u00fcksekse ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 da o kadar y\u00fcksektir.<\/p>\n<p> \u00d6rne\u011fin bir olay\u0131n olas\u0131l\u0131k de\u011feri 0,50 ise olay\u0131n ger\u00e7ekle\u015fme ihtimali %50 demektir. Yani ortalama olarak olay iki denemede bir ger\u00e7ekle\u015fecektir.<\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rastgele-deneyim\/\">Rastgele bir deneyin<\/a> sonucunun ger\u00e7ekle\u015fece\u011finden emin olmad\u0131\u011f\u0131m\u0131zda, bu sonucun elde edilme olas\u0131l\u0131\u011f\u0131n\u0131 ve ne kadar risk al\u0131naca\u011f\u0131n\u0131 bilmek i\u00e7in bu sonucun ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayabiliriz. \u00d6rne\u011fin pokerde izlenecek stratejiyi belirlemek i\u00e7in belirli kartlar\u0131 alma olas\u0131l\u0131klar\u0131 hesaplan\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-de-un-evento\"><\/span> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131 i\u00e7in form\u00fcl<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir olay\u0131n olas\u0131l\u0131\u011f\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\u00f6yleyen <a href=\"https:\/\/statorials.org\/tr\/laplace-kurali-veya-laplace-yasasi\/\">Laplace kural\u0131yla<\/a> hesaplan\u0131r.<\/p>\n<p> Bu nedenle <strong>bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n form\u00fcl\u00fc<\/strong> \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-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 style=\"margin-bottom:10px\"> Alt\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:10px\"> <span style=\"color:#101010;font-weight: normal;\">P(A), A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:10px\"> <span style=\"color:#101010;font-weight: normal;\">Olumlu durumlar, s\u00f6z konusu olay\u0131n ko\u015fullar\u0131n\u0131 kar\u015f\u0131layan t\u00fcm sonu\u00e7lard\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:10px\"> <span style=\"color:#101010;font-weight: normal;\">Olas\u0131 durumlar, meydana gelebilecek toplam sonu\u00e7 say\u0131s\u0131d\u0131r.<\/span><\/li>\n<\/ul>\n<p> Ancak farkl\u0131 olas\u0131l\u0131k t\u00fcrlerinin bulundu\u011funu ve bu nedenle bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131lacak form\u00fcl\u00fcn ko\u015fullara g\u00f6re de\u011fi\u015febilece\u011fini unutmamal\u0131s\u0131n\u0131z. Farkl\u0131 olas\u0131l\u0131k t\u00fcrlerinin neler oldu\u011funu burada 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\/olasilik-turleri\/\">Olas\u0131l\u0131k t\u00fcrleri<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-probabilidad-de-un-evento\"><\/span> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplama \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n form\u00fcl\u00fcn\u00fcn ne oldu\u011funu g\u00f6rd\u00fckten sonra, bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rebilmeniz i\u00e7in sizi a\u015fa\u011f\u0131da somut bir \u00f6rnekle b\u0131rak\u0131yoruz.<\/p>\n<ul>\n<li> Bir zar\u0131n at\u0131lmas\u0131yla \u00e7ift say\u0131 gelme olas\u0131l\u0131\u011f\u0131 ka\u00e7t\u0131r?<\/li>\n<\/ul>\n<p> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in Laplace kural\u0131n\u0131n a\u015fa\u011f\u0131daki 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-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> Bu durumda zarda \u00fc\u00e7 \u00e7ift say\u0131 (2, 4, 6) oldu\u011fundan olumlu durum say\u0131s\u0131 3&#8217;t\u00fcr. \u00d6te yandan olas\u0131 durumlar\u0131n say\u0131s\u0131 t\u00fcm olas\u0131 sonu\u00e7lara e\u015fittir, yani 6 \u00e7\u00fcnk\u00fc zar\u0131n alt\u0131 y\u00fcz\u00fc vard\u0131r (1, 2, 3, 4, 5, 6). Yani al\u0131\u015ft\u0131rman\u0131n bizden yapmam\u0131z\u0131 istedi\u011fi olay\u0131n 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-6122d4de7d9271015aede4a33b6862a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{n\\'umero par})=\\cfrac{3}{6}=0,50\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"210\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Bu nedenle, zar at\u0131\u015f\u0131nda \u00e7ift say\u0131 gelme olas\u0131l\u0131\u011f\u0131 0,50 veya e\u015fde\u011fer olarak %50&#8217;dir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-probabilidad-de-un-evento\"><\/span> Bir olay hesaplay\u0131c\u0131s\u0131n\u0131n olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in olumlu durumlar\u0131n say\u0131s\u0131n\u0131 ve olas\u0131 durumlar\u0131n say\u0131s\u0131n\u0131 a\u015fa\u011f\u0131daki hesaplay\u0131c\u0131ya girin.<\/p>\n<form action=\"\" method=\"post\">\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> Olumlu durum say\u0131s\u0131: <input name=\"casosfavorables\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero de casos favorables aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span><\/div>\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> Olas\u0131 vakalar\u0131n say\u0131s\u0131: <input name=\"casosposibles\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero de casos posibles aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/span> <\/div>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Olas\u0131l\u0131\u011f\u0131 hesapla\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-de-dos-eventos\"><\/span> iki olay\u0131n olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u015eu ana kadar bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l bulunaca\u011f\u0131n\u0131 g\u00f6rd\u00fck ancak iki olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n hesaplanmas\u0131 farkl\u0131 bir \u015fekilde yap\u0131l\u0131r.<\/p>\n<p> Daha sonra, iki olas\u0131 olaydan en az birinin meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 (iki olay\u0131n birle\u015fimi), ard\u0131ndan iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 (iki olay\u0131n kesi\u015fimi) nas\u0131l belirleyece\u011fimizi g\u00f6rece\u011fiz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"union-de-dos-eventos\"><\/span> \u0130ki olay\u0131n birle\u015fimi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0130ki olay\u0131n birle\u015fimi, iki olaydan en az birinin meydana gelmesi anlam\u0131na gelir. Yani olaylardan biri veya her ikisi ayn\u0131 anda meydana gelebilir.<\/p>\n<p> \u0130ki olay\u0131n birle\u015fimi toplam kural\u0131 (veya toplama kural\u0131) kullan\u0131larak hesaplan\u0131r; bu kural, 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 toplam\u0131 eksi her iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131na e\u015fit oldu\u011funu s\u00f6yler. Ayn\u0131 zaman. ayn\u0131 zamanda.<\/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\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interseccion-de-dos-eventos\"><\/span> iki olay\u0131n kesi\u015fmesi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0130ki olay\u0131n kesi\u015fmesi, iki farkl\u0131 olay\u0131n ayn\u0131 anda meydana gelmesi anlam\u0131na gelir. Bu durumda sadece her iki olay\u0131n ger\u00e7ekle\u015fmesi dikkate al\u0131n\u0131r; bunlardan yaln\u0131zca birinin ger\u00e7ekle\u015fmesi ge\u00e7erli de\u011fildir.<\/p>\n<p> Dolay\u0131s\u0131yla, iki olay\u0131n kesi\u015fimi, 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\u00f6yleyen \u00e7arpma kural\u0131 (veya \u00e7arp\u0131m kural\u0131) kullan\u0131larak bulunur.<\/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\u0131n \u00e7arp\u0131m kural\u0131 form\u00fcl\u00fcn\u00fcn ne oldu\u011funu ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen al\u0131\u015ft\u0131rmalar\u0131 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\u0131na ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n ne oldu\u011fu a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 nas\u0131l hesaplayaca\u011f\u0131n\u0131z\u0131, \u00e7\u00f6z\u00fcml\u00fc \u00f6rnekleri ve ayr\u0131ca herhangi bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in \u00e7evrimi\u00e7i bir hesap makinesini bulacaks\u0131n\u0131z. Bir olay\u0131n olas\u0131l\u0131\u011f\u0131 ne kadard\u0131r? Bir olay\u0131n olas\u0131l\u0131\u011f\u0131, istatistiksel bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren bir de\u011ferdir. Bir olay\u0131n olas\u0131l\u0131k de\u011feri 0 ( imkans\u0131z olay ) [&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-384","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 Bir olay\u0131n olas\u0131l\u0131\u011f\u0131<\/title>\n<meta name=\"description\" content=\"Burada bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n ne oldu\u011funu, bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 (form\u00fcl), \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rnekleri ve \u00e7evrimi\u00e7i hesap makinesini bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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