{"id":46,"date":"2023-08-06T04:35:57","date_gmt":"2023-08-06T04:35:57","guid":{"rendered":"https:\/\/statorials.org\/tr\/klasik-olasilik\/"},"modified":"2023-08-06T04:35:57","modified_gmt":"2023-08-06T04:35:57","slug":"klasik-olasilik","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/klasik-olasilik\/","title":{"rendered":"Klasik olas\u0131l\u0131k"},"content":{"rendered":"<p>Burada klasik olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu, klasik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve somut bir \u00f6rnek bulacaks\u0131n\u0131z. Ayr\u0131ca klasik olas\u0131l\u0131k ile di\u011fer olas\u0131l\u0131k t\u00fcrleri aras\u0131ndaki farklar\u0131 da g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-clasica\"><\/span> Klasik olas\u0131l\u0131k nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Klasik olas\u0131l\u0131k,<\/strong> bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Klasik olas\u0131l\u0131k, bu olay\u0131n olumlu durum say\u0131s\u0131n\u0131n toplam olas\u0131 durum say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n<p> Klasik olas\u0131l\u0131k ayn\u0131 zamanda <strong>teorik olas\u0131l\u0131k<\/strong> veya <strong>a priori olas\u0131l\u0131k<\/strong> olarak da bilinir.<\/p>\n<p> Klasik olas\u0131l\u0131k 0 ile 1 aras\u0131nda bir say\u0131d\u0131r. Bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ne kadar y\u00fcksekse klasik olas\u0131l\u0131k da o kadar b\u00fcy\u00fck olacakt\u0131r; tersine, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 ne kadar d\u00fc\u015f\u00fck olursa de\u011fer de o kadar d\u00fc\u015f\u00fck olur. klasik olas\u0131l\u0131k olacakt\u0131r.<\/p>\n<p> Di\u011fer olas\u0131l\u0131k t\u00fcrlerinden farkl\u0131 olarak bir olay\u0131n klasik olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in deneye gerek yoktur; bu teorik bir hesaplamad\u0131r. A\u015fa\u011f\u0131da bu kavram\u0131 daha derinlemesine inceleyece\u011fiz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-clasica\"><\/span> Klasik olas\u0131l\u0131k form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Klasik olas\u0131l\u0131k form\u00fcl\u00fc<\/strong> , bir olay\u0131n olumlu durum say\u0131s\u0131n\u0131n deneydeki toplam olay say\u0131s\u0131na b\u00f6l\u00fcnmesiyle elde edilir.<\/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-47eefb1b0f197dfabcdb701b4858c3b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(A)=\\cfrac{\\text{n\\'umero de casos favorables al evento A}}{\\text{n\\'umero total de casos}}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"372\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Bu form\u00fcl ayn\u0131 zamanda <strong>Laplace kural\u0131<\/strong> (veya Laplace yasas\u0131) olarak da bilinir, \u00e7\u00fcnk\u00fc bunu ilk kez 1812&#8217;de <em>Analitik Olas\u0131l\u0131k Teorisi<\/em> yay\u0131n\u0131nda \u00f6neren sayg\u0131n Frans\u0131z matematik\u00e7idir.<\/p>\n<p> Bu form\u00fcl\u00fcn kullan\u0131labilmesi i\u00e7in \u00f6rnek uzaydaki t\u00fcm olaylar\u0131n e\u015f olas\u0131l\u0131kl\u0131 olmas\u0131, yani <strong>e\u015f olas\u0131l\u0131kl\u0131 bir \u00f6rnek uzay<\/strong> olmas\u0131 gerekti\u011fi dikkate al\u0131nmal\u0131d\u0131r. Bu terimin ne anlama geldi\u011fini bilmiyorsan\u0131z devam etmeden \u00f6nce a\u015fa\u011f\u0131daki ba\u011flant\u0131ya g\u00f6z atman\u0131z\u0131 \u00f6neririm: <\/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 nedir?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-probabilidad-clasica\"><\/span> Klasik olas\u0131l\u0131k \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A\u015fa\u011f\u0131da klasik olas\u0131l\u0131\u011f\u0131n tan\u0131m\u0131n\u0131 dikkate alarak bu t\u00fcr olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131na dair bir \u00f6rnek a\u00e7\u0131klayaca\u011f\u0131z. B\u00f6ylece klasik olas\u0131l\u0131\u011f\u0131n anlam\u0131n\u0131 daha iyi anlayacaks\u0131n\u0131z.<\/p>\n<ul>\n<li> Zar at\u0131ld\u0131\u011f\u0131nda <em>\u201c5 rakam\u0131n\u0131n at\u0131lmas\u0131\u201d<\/em> olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplay\u0131n. Daha sonra <em>\u201c4&#8217;ten k\u00fc\u00e7\u00fck bir say\u0131 alma\u201d<\/em> olas\u0131l\u0131\u011f\u0131n\u0131 da belirleyin.<\/li>\n<\/ul>\n<p> Bu durumda, alt\u0131 olas\u0131 sonucu olan (1, 2, 3, 4, 5 ve 6) bir zar\u0131n at\u0131lmas\u0131yla ilgili rastgele deneyini analiz etmek istiyoruz. Zar\u0131n hileli olmad\u0131\u011f\u0131n\u0131 ve iyi durumda oldu\u011funu varsayd\u0131\u011f\u0131m\u0131z i\u00e7in, deneyin t\u00fcm temel olaylar\u0131n\u0131n e\u015fit derecede olas\u0131 oldu\u011funu d\u00fc\u015f\u00fcnebiliriz. Bu nedenle klasik olas\u0131l\u0131klar\u0131 t\u00fcretmek i\u00e7in Laplace kural\u0131n\u0131 kullanabiliriz.<\/p>\n<p> <em>&#8220;5 say\u0131s\u0131n\u0131 elde etme&#8221;<\/em> durumunda, zar\u0131n 5 numaral\u0131 y\u00fcz\u00fcn\u00fc elde etti\u011fimiz tek olumlu durum vard\u0131r. Ancak alt\u0131 olas\u0131 sonu\u00e7 vard\u0131r, dolay\u0131s\u0131yla olay\u0131n klasik olas\u0131l\u0131\u011f\u0131 \u015f\u00f6yle olacakt\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-a3bb38e1b0cea46c13a67fd1b06e3236_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{n\\'umero 5})&amp;=\\cfrac{\\text{n\\'umero de casos favorables}}{\\text{n\\'umero total de casos}}\\\\[2ex] &amp;= \\cfrac{1}{6}\\\\[2ex] &amp;=0,167\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"337\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u00d6te yandan klasik <em>\u201c4&#8217;ten k\u00fc\u00e7\u00fck bir say\u0131 elde etme\u201d<\/em> olas\u0131l\u0131\u011f\u0131n\u0131 da bulmak istiyoruz. Bu durum bile\u015fik bir olayd\u0131r ve \u00fc\u00e7 olas\u0131 olumlu durum vard\u0131r, \u00e7\u00fcnk\u00fc olay 1, 2 veya 3 say\u0131s\u0131n\u0131n ortaya \u00e7\u0131kmas\u0131 durumunda ger\u00e7ekle\u015fecektir. Dolay\u0131s\u0131yla olay\u0131n klasik olas\u0131l\u0131\u011f\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-1d6fbd15e91770e00648a9a44a286432_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(\\text{n\\'umero menor que 4})&amp;=\\cfrac{\\text{n\\'umero de casos favorables}}{\\text{n\\'umero total de casos}}\\\\[2ex] &amp;= \\cfrac{3}{6}\\\\[2ex] &amp;=0,5\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"424\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-clasica-y-probabilidad-frecuencial\"><\/span> Klasik olas\u0131l\u0131k ve frekans olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Klasik olas\u0131l\u0131k ile frekans olas\u0131l\u0131\u011f\u0131 (veya ampirik olas\u0131l\u0131k) aras\u0131ndaki fark<\/strong> , klasik olas\u0131l\u0131\u011f\u0131n herhangi bir deney yap\u0131lmadan hesaplanmas\u0131, yani bir olay\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in mant\u0131\u011f\u0131n kullan\u0131lmas\u0131d\u0131r. deney ger\u00e7ekle\u015ftirilir ve sonu\u00e7lardan meydana gelme olas\u0131l\u0131\u011f\u0131 hesaplan\u0131r.<\/p>\n<p> Ancak bir olay\u0131n s\u0131kl\u0131k olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in tek bir deney yapmak yeterli olmay\u0131p, ayn\u0131 deneyin birka\u00e7 kez tekrarlanmas\u0131 gerekir. Deney ne kadar \u00e7ok tekrarlan\u0131rsa frekans olas\u0131l\u0131\u011f\u0131 o kadar do\u011fru olacakt\u0131r. Deneyleri h\u0131zl\u0131 bir \u015fekilde sim\u00fcle etmek i\u00e7in genellikle binlerce bilgisayar program\u0131n\u0131n kullan\u0131lmas\u0131n\u0131n nedeni budur.<\/p>\n<p> G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi frekans olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak kolay de\u011fil. Bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131na dair ad\u0131m ad\u0131m bir \u00f6rne\u011fi 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\/frekans-frekansi-olasiligi-1\/\">frekans olas\u0131l\u0131k \u00f6rne\u011fi<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-clasica-y-probabilidad-condicional\"><\/span> Klasik olas\u0131l\u0131k ve ko\u015fullu olas\u0131l\u0131k<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ko\u015fullu olas\u0131l\u0131k<\/strong> (veya ko\u015fullu olas\u0131l\u0131k), klasik olas\u0131l\u0131ktan tamamen farkl\u0131 bir olas\u0131l\u0131k t\u00fcr\u00fcd\u00fcr. Klasik olas\u0131l\u0131kta sadece ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 hesaplanacak olay dikkate al\u0131n\u0131rken, ko\u015fullu olas\u0131l\u0131kta daha \u00f6nceki olaylar da dikkate al\u0131n\u0131r.<\/p>\n<p> Yani bir olay\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131 daha \u00f6nce meydana gelen olaylara ba\u011fl\u0131d\u0131r. \u00d6rne\u011fin, bir \u0130spanyol destesinden kalp kart\u0131 \u00e7ekilme olas\u0131l\u0131\u011f\u0131, daha \u00f6nce bir kalp kart\u0131n\u0131n \u00e7ekilip \u00e7ekilmedi\u011fine veya ba\u015fka t\u00fcrde bir kart\u0131n \u00e7ekilip \u00e7ekilmedi\u011fine ba\u011fl\u0131 olarak daha d\u00fc\u015f\u00fck veya daha y\u00fcksek olacakt\u0131r.<\/p>\n<p> Ko\u015fullu olas\u0131l\u0131k hesaplamas\u0131, klasik olas\u0131l\u0131k hesaplamas\u0131na g\u00f6re daha zordur ve ayr\u0131ca di\u011fer kavramlar\u0131n da \u00f6nceden bilinmesi gerekir. Buraya t\u0131klayarak bir olay\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 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 form\u00fcl\u00fc<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Burada klasik olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu, klasik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 ve somut bir \u00f6rnek bulacaks\u0131n\u0131z. Ayr\u0131ca klasik olas\u0131l\u0131k ile di\u011fer olas\u0131l\u0131k t\u00fcrleri aras\u0131ndaki farklar\u0131 da g\u00f6rebileceksiniz. Klasik olas\u0131l\u0131k nedir? Klasik olas\u0131l\u0131k, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Klasik olas\u0131l\u0131k, bu olay\u0131n olumlu durum say\u0131s\u0131n\u0131n toplam olas\u0131 durum say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir. Klasik olas\u0131l\u0131k ayn\u0131 [&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-46","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 Klasik olas\u0131l\u0131k nedir? 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Klasik olas\u0131l\u0131\u011f\u0131n \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rnekleriyle.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/klasik-olasilik\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-06T04:35:57+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-47eefb1b0f197dfabcdb701b4858c3b5_l3.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/klasik-olasilik\/\",\"url\":\"https:\/\/statorials.org\/tr\/klasik-olasilik\/\",\"name\":\"\u25b7 Klasik olas\u0131l\u0131k nedir? (tan\u0131m ve \u00f6rnekler)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-06T04:35:57+00:00\",\"dateModified\":\"2023-08-06T04:35:57+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Klasik olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) a\u00e7\u0131kl\u0131yoruz. 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