{"id":391,"date":"2023-08-01T06:26:21","date_gmt":"2023-08-01T06:26:21","guid":{"rendered":"https:\/\/statorials.org\/tr\/olasiliklarin-hesaplanmasi\/"},"modified":"2023-08-01T06:26:21","modified_gmt":"2023-08-01T06:26:21","slug":"olasiliklarin-hesaplanmasi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olasiliklarin-hesaplanmasi\/","title":{"rendered":"Olas\u0131l\u0131klar\u0131n hesaplanmas\u0131"},"content":{"rendered":"<p>Bu makalede olay olas\u0131l\u0131klar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olas\u0131l\u0131klar\u0131 hesaplamak i\u00e7in bir form\u00fcl, olas\u0131l\u0131k hesaplama \u00f6rnekleri ve ayr\u0131ca herhangi bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in bir \u00e7evrimi\u00e7i hesap makinesi bulacaks\u0131n\u0131z.<\/p>\n<p> Olas\u0131l\u0131k hesaplamas\u0131n\u0131n bir\u00e7ok uygulamaya sahip oldu\u011funu belirtmek gerekir; \u00f6rne\u011fin bir yat\u0131r\u0131m\u0131n ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131, bir g\u00fcn ya\u011fmur ya\u011fma olas\u0131l\u0131\u011f\u0131n\u0131, bir ki\u015finin belirli bir hastal\u0131ktan etkilenme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131labilir. belirli semptomlar vb. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-calculo-de-probabilidades\"><\/span> Olas\u0131l\u0131k Hesaplama Form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in olumlu durum say\u0131s\u0131n\u0131 olas\u0131 durum say\u0131s\u0131na b\u00f6lmeniz gerekir. Bu nedenle <strong>olas\u0131l\u0131klar\u0131 hesaplaman\u0131n form\u00fcl\u00fc<\/strong> Olas\u0131l\u0131k = Olumlu Durumlar \/ Olas\u0131 Durumlar&#8217;d\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-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> Olas\u0131l\u0131\u011f\u0131n de\u011ferinin 0 ile 1 aras\u0131nda bir say\u0131 oldu\u011funu unutmay\u0131n. Olas\u0131l\u0131k ne kadar y\u00fcksekse olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 da o kadar y\u00fcksektir. Yani 0 olas\u0131l\u0131\u011f\u0131 olay\u0131n ger\u00e7ekle\u015femeyece\u011fi, 1 olas\u0131l\u0131\u011f\u0131 ise olay\u0131n her zaman ger\u00e7ekle\u015fece\u011fi anlam\u0131na gelir.<\/p>\n<p> \u00d6rne\u011fin, yaz\u0131 tura at\u0131ld\u0131\u011f\u0131nda tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in olumlu durumlar\u0131n say\u0131s\u0131n\u0131 (1) olas\u0131 durumlar\u0131n say\u0131s\u0131na (2) b\u00f6lmeniz gerekir. Dolay\u0131s\u0131yla tura gelme olas\u0131l\u0131\u011f\u0131 1\/2 = 0,50&#8217;dir.<\/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-12569f67a825f820238af78b037352f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara})=\\cfrac{\\text{casos favorables}}{\\text{casos posibles}}=\\cfrac{1}{2}=0,50\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"301\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131, sonucun 100 ile \u00e7arp\u0131lmas\u0131yla y\u00fczde olarak da ifade edilebilir.<\/p>\n<p> Olaylar\u0131n b\u00fcy\u00fck \u00e7o\u011funlu\u011funun olas\u0131l\u0131klar\u0131n\u0131 hesaplamam\u0131z\u0131 sa\u011flayan bu form\u00fcle, olas\u0131l\u0131k teorisinin temellerini atan matematik\u00e7i Pierre-Simon Laplace&#8217;\u0131n (1749-1827) an\u0131s\u0131na Laplace kural\u0131 ad\u0131 verilmektedir. <\/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<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-calculos-de-probabilidades\"><\/span> Olas\u0131l\u0131k hesaplama \u00f6rnekleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k olas\u0131l\u0131k hesaplamas\u0131n\u0131n ne oldu\u011funu g\u00f6rd\u00fc\u011f\u00fcm\u00fcze g\u00f6re, kavram\u0131 daha iyi anlamak i\u00e7in a\u015fa\u011f\u0131da farkl\u0131 olaylar\u0131n olas\u0131l\u0131klar\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131na dair birka\u00e7 \u00f6rnek verilmi\u015ftir.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1-lanzamiento-de-un-dado\"><\/span> \u00d6rnek 1: Bir zar\u0131n yuvarlanmas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\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 yukar\u0131da g\u00f6rd\u00fc\u011f\u00fcm\u00fcz form\u00fcl\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, bir zar at\u0131ld\u0131\u011f\u0131nda \u00e7ift say\u0131 gelme olas\u0131l\u0131\u011f\u0131 0,50 veya buna e\u015fde\u011fer olarak %50&#8217;dir. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2-bolas-de-una-bolsa\"><\/span> \u00d6rnek 2: torbadaki toplar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Bo\u015f bir kutuya 5 mavi top, 4 ye\u015fil top ve 2 sar\u0131 top koyuyoruz. Rastgele bir top \u00e7ekildi\u011finde mavi olma olas\u0131l\u0131\u011f\u0131 nedir?<\/li>\n<\/ul>\n<p> Bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in yaz\u0131n\u0131n ba\u015f\u0131nda a\u00e7\u0131klanan form\u00fcl\u00fc uygulamal\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-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 kutuya 5 mavi top koydu\u011fumuz i\u00e7in olumlu durum say\u0131s\u0131 5 olur. \u00d6te yandan olas\u0131 kutu say\u0131s\u0131 yerle\u015ftirilen t\u00fcm toplar\u0131n toplam\u0131d\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-613fe8177cd01f9796d49b5ea92590c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{bola azul})=\\cfrac{5}{5+4+2}=\\cfrac{5}{11}=0,45\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"294\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> Buna g\u00f6re kutudan mavi top \u00e7ekilme olas\u0131l\u0131\u011f\u0131 0,45 veya y\u00fczde olarak ifade edilirse %45&#8217;tir. <\/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=\"calculadora-de-probabilidades\"><\/span>oran hesaplay\u0131c\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<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=\"calculo-de-la-probabilidad-condicionada\"><\/span> Ko\u015fullu Olas\u0131l\u0131k Hesaplamas\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ko\u015fullu olas\u0131l\u0131k olarak da adland\u0131r\u0131lan ko\u015fullu olas\u0131l\u0131k, ba\u015fka bir B olay\u0131n\u0131n meydana gelmesi durumunda A olay\u0131n\u0131n da meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirtir. Yani ko\u015fullu olas\u0131l\u0131k P(A|B), A olay\u0131n\u0131n B olay\u0131 ger\u00e7ekle\u015ftikten sonra meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 ifade eder.<\/p>\n<p> Ko\u015fullu olas\u0131l\u0131k, iki olay aras\u0131nda dikey bir \u00e7ubukla yaz\u0131l\u0131r: P(A|B) ve \u015funu okur: &#8220;B olay\u0131 verildi\u011finde A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131&#8221;.<\/p>\n<p> Dolay\u0131s\u0131yla, belirli bir B olay\u0131n\u0131n A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131, A olay\u0131 ile B olay\u0131 aras\u0131ndaki kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n B olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/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-f95773f97f65355e94817757e7bc3e76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A|B)=\\cfrac{P(A\\cap B)}{P(B)}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"161\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Bir olay\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131na dair \u00f6rnekleri 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\/kosullu-kosullu-olasilik\/\">Ko\u015fullu olas\u0131l\u0131k \u00f6rne\u011fi<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede olay olas\u0131l\u0131klar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece olas\u0131l\u0131klar\u0131 hesaplamak i\u00e7in bir form\u00fcl, olas\u0131l\u0131k hesaplama \u00f6rnekleri ve ayr\u0131ca herhangi bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in bir \u00e7evrimi\u00e7i hesap makinesi bulacaks\u0131n\u0131z. Olas\u0131l\u0131k hesaplamas\u0131n\u0131n bir\u00e7ok uygulamaya sahip oldu\u011funu belirtmek gerekir; \u00f6rne\u011fin bir yat\u0131r\u0131m\u0131n ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131, bir g\u00fcn ya\u011fmur ya\u011fma olas\u0131l\u0131\u011f\u0131n\u0131, bir ki\u015finin belirli bir hastal\u0131ktan etkilenme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-391","post","type-post","status-publish","format-standard","hentry","category-kategorize-edilmemis"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Olas\u0131l\u0131klar\u0131n hesaplanmas\u0131: form\u00fcl, \u00f6rnekler ve hesap makinesi<\/title>\n<meta name=\"description\" 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