{"id":44,"date":"2023-08-06T05:29:40","date_gmt":"2023-08-06T05:29:40","guid":{"rendered":"https:\/\/statorials.org\/tr\/teorik-olasilik-1\/"},"modified":"2023-08-06T05:29:40","modified_gmt":"2023-08-06T05:29:40","slug":"teorik-olasilik-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/teorik-olasilik-1\/","title":{"rendered":"Teorik olas\u0131l\u0131k"},"content":{"rendered":"<p>Bu yaz\u0131da teorik olas\u0131l\u0131\u011f\u0131n anlam\u0131n\u0131 ve teorik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 \u00f6\u011freneceksiniz. Ayr\u0131ca bir olay\u0131n teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplaman\u0131n somut bir \u00f6rne\u011fini g\u00f6rebileceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-teorica\"><\/span> Teorik olas\u0131l\u0131k nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Teorik olas\u0131l\u0131k,<\/strong> bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Bir olay\u0131n teorik olas\u0131l\u0131\u011f\u0131, s\u00f6z konusu olay\u0131n olumlu durumlar\u0131n\u0131n say\u0131s\u0131n\u0131n toplam olas\u0131 durum say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n<p> Teorik olas\u0131l\u0131k ayn\u0131 zamanda <strong>klasik olas\u0131l\u0131k<\/strong> veya <strong>a priori olas\u0131l\u0131k<\/strong> olarak da bilinir.<\/p>\n<p> Ek olarak, teorik olas\u0131l\u0131k 0 ile 1 aras\u0131nda bir de\u011ferdir. Mant\u0131ksal olarak de\u011fer ne kadar b\u00fcy\u00fck olursa, s\u00f6z konusu olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 da o kadar y\u00fcksek olur; s\u0131f\u0131r, ger\u00e7ekle\u015femeyecek bir olay ve bir ise ger\u00e7ekle\u015fecek bir olayd\u0131r. \u00fcretecek. her zaman olur. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-teorica\"><\/span> Teorik olas\u0131l\u0131k form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Teorik olas\u0131l\u0131k form\u00fcl\u00fc,<\/strong> bir olay\u0131n olumlu durumlar\u0131n\u0131n 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. A\u00e7\u0131k\u00e7as\u0131, bu form\u00fcl\u00fcn bu \u015fekilde adland\u0131r\u0131lmas\u0131n\u0131n nedeni, kural\u0131 ilk olarak The <em>Analytical Theory of Probability<\/em> (1812) adl\u0131 yay\u0131n\u0131nda \u00f6neren ki\u015finin Pierre-Siman Laplace olmas\u0131d\u0131r.<\/p>\n<p> Bu form\u00fcl\u00fcn ancak \u00f6rnek uzaydaki temel olaylar\u0131n e\u015f olas\u0131l\u0131kl\u0131 olmas\u0131, yani <strong>e\u015f olas\u0131l\u0131kl\u0131 bir \u00f6rnek uzay<\/strong> olmas\u0131 durumunda kullan\u0131labilece\u011fini unutmamal\u0131s\u0131n\u0131z. Bu terimin ne anlama geldi\u011fini bilmiyorsan\u0131z, olas\u0131l\u0131\u011f\u0131n temel bir kavram\u0131 oldu\u011fundan a\u00e7\u0131klamay\u0131 okumaya devam etmeden \u00f6nce a\u015fa\u011f\u0131daki ba\u011flant\u0131y\u0131 ziyaret etmenizi \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\/\">\u00f6rnek uzay (olas\u0131l\u0131k)<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-probabilidad-teorica\"><\/span> Teorik olas\u0131l\u0131k \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Teorik olas\u0131l\u0131\u011f\u0131n tan\u0131m\u0131n\u0131 g\u00f6rd\u00fckten sonra bu b\u00f6l\u00fcmde bu t\u00fcr olas\u0131l\u0131\u011f\u0131n bir \u00f6rne\u011fini \u00e7\u00f6zece\u011fiz.<\/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> Deneyimin t\u00fcm temel olaylar\u0131 (1, 2, 3, 4, 5 ve 6) e\u015fit olas\u0131l\u0131kl\u0131d\u0131r. Bu nedenle olaylar\u0131n teorik olas\u0131l\u0131klar\u0131n\u0131 bulmak i\u00e7in Laplace kural\u0131n\u0131 uygulayabiliriz.<\/p>\n<p> <em>&#8220;5 say\u0131s\u0131n\u0131 elde etme&#8221; durumunda,<\/em> yaln\u0131zca tek bir olumlu durum vard\u0131r: 5 say\u0131s\u0131n\u0131 elde etme. Ancak alt\u0131 olas\u0131 sonu\u00e7 vard\u0131r, dolay\u0131s\u0131yla teorik olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in birini alt\u0131ya b\u00f6lmeniz 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-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> A\u00e7\u0131klamada ayr\u0131ca bizden <em>&#8220;4&#8217;ten k\u00fc\u00e7\u00fck bir say\u0131 alman\u0131n&#8221;<\/em> teorik olas\u0131l\u0131\u011f\u0131n\u0131 bulmam\u0131z isteniyor. Bu olay bile\u015fiktir ve 1, 2 veya 3 rakam\u0131n\u0131n ortaya \u00e7\u0131kmas\u0131 durumunda olay meydana gelece\u011fi i\u00e7in \u00fc\u00e7 olas\u0131 olumlu durum vard\u0131r. Dolay\u0131s\u0131yla olay\u0131n teorik 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-teorica-y-probabilidad-frecuencial\"><\/span> Teorik olas\u0131l\u0131k ve frekans olas\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Teorik olas\u0131l\u0131k kavram\u0131n\u0131 anlamay\u0131 bitirmek i\u00e7in, teorik olas\u0131l\u0131k ile frekans olas\u0131l\u0131\u011f\u0131 aras\u0131ndaki fark\u0131n ne oldu\u011funa bakal\u0131m, \u00e7\u00fcnk\u00fc bunlar\u0131n iki z\u0131t olas\u0131l\u0131k t\u00fcr\u00fc oldu\u011funu s\u00f6yleyebiliriz.<\/p>\n<p> <strong>Teorik olas\u0131l\u0131k ile frekans olas\u0131l\u0131\u011f\u0131 (veya ampirik olas\u0131l\u0131k) aras\u0131ndaki fark,<\/strong> teorik olas\u0131l\u0131\u011f\u0131n mant\u0131k ve teori kullan\u0131larak hesaplanmas\u0131, frekans olas\u0131l\u0131\u011f\u0131n\u0131n ise bir deneyden elde edilen sonu\u00e7lar kullan\u0131larak hesaplanmas\u0131d\u0131r.<\/p>\n<p> Frekans olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in tek bir deney yapmak yeterli de\u011fildir, \u00e7\u00fcnk\u00fc ko\u015fulland\u0131r\u0131labilir ve bu durumda g\u00fcvenilmez sonu\u00e7lar elde edebiliriz. Aksine, daha g\u00fcvenilir olas\u0131l\u0131klar elde etmek i\u00e7in bir\u00e7ok deneyin sim\u00fcle edilmesi gerekir. Asl\u0131nda ne kadar \u00e7ok deney yaparsak frekans olas\u0131l\u0131\u011f\u0131n\u0131n do\u011frulu\u011fu o kadar artar.<\/p>\n<p> Bu nedenle frekans olas\u0131l\u0131\u011f\u0131n\u0131n hesaplanmas\u0131 teorik olas\u0131l\u0131\u011fa g\u00f6re daha karma\u015f\u0131kt\u0131r. Ancak burada ad\u0131m ad\u0131m a\u00e7\u0131klanan birka\u00e7 \u00f6rne\u011fi 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\u0131\u011f\u0131n\u0131n \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rnekleri<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131da teorik olas\u0131l\u0131\u011f\u0131n anlam\u0131n\u0131 ve teorik olas\u0131l\u0131\u011f\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 \u00f6\u011freneceksiniz. Ayr\u0131ca bir olay\u0131n teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplaman\u0131n somut bir \u00f6rne\u011fini g\u00f6rebileceksiniz. Teorik olas\u0131l\u0131k nedir? Teorik olas\u0131l\u0131k, bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Bir olay\u0131n teorik olas\u0131l\u0131\u011f\u0131, s\u00f6z konusu olay\u0131n olumlu durumlar\u0131n\u0131n say\u0131s\u0131n\u0131n toplam olas\u0131 durum say\u0131s\u0131na b\u00f6l\u00fcnmesine e\u015fittir. Teorik olas\u0131l\u0131k ayn\u0131 zamanda [&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-44","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 Teorik olas\u0131l\u0131k nedir? 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Teorik olas\u0131l\u0131\u011f\u0131n \u00e7\u00f6z\u00fclm\u00fc\u015f \u00f6rnekleriyle.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/teorik-olasilik-1\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-06T05:29:40+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=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/teorik-olasilik-1\/\",\"url\":\"https:\/\/statorials.org\/tr\/teorik-olasilik-1\/\",\"name\":\"\u25b7 Teorik olas\u0131l\u0131k nedir? 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