{"id":579,"date":"2023-07-29T10:51:25","date_gmt":"2023-07-29T10:51:25","guid":{"rendered":"https:\/\/statorials.org\/tr\/teorik-olasilik\/"},"modified":"2023-07-29T10:51:25","modified_gmt":"2023-07-29T10:51:25","slug":"teorik-olasilik","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/teorik-olasilik\/","title":{"rendered":"Teorik olas\u0131l\u0131k: tan\u0131m + \u00f6rnekler"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Olas\u0131l\u0131k, istatistikte belirli olaylar\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klayan bir konudur. Olas\u0131l\u0131k hakk\u0131nda konu\u015ftu\u011fumuzda genellikle iki t\u00fcrden birine ba\u015fvururuz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Teorik olas\u0131l\u0131k<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Teorik olas\u0131l\u0131k, saf matemati\u011fe dayal\u0131 olarak bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r. <em>A<\/em> olay\u0131n\u0131n meydana gelme teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in form\u00fcl \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>A<\/em> ) = istenen sonu\u00e7lar\u0131n say\u0131s\u0131 \/ olas\u0131 sonu\u00e7lar\u0131n toplam say\u0131s\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, zar\u0131n at\u0131\u015ftan sonra &#8220;2&#8221;ye gelme olas\u0131l\u0131\u011f\u0131 teorik olarak \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>2&#8217;ye inin<\/em> ) = (zarlar\u0131n 2&#8217;ye d\u00fc\u015febilece\u011fi tek yol) \/ (zarlar\u0131n d\u00fc\u015febilece\u011fi alt\u0131 olas\u0131 taraf) = <strong>1\/6<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Deneysel olas\u0131l\u0131k<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Deneysel olas\u0131l\u0131k, bir deneyde do\u011frudan g\u00f6zlemledi\u011finiz bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r. <em>A<\/em> olay\u0131n\u0131n deneysel olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in form\u00fcl \u015f\u00f6yledir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>A<\/em> ) = olay\u0131n meydana gelme say\u0131s\u0131 \/ toplam deneme say\u0131s\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir zar\u0131 11 kez att\u0131\u011f\u0131m\u0131z\u0131 ve zar\u0131n \u00fc\u00e7 kez &#8220;2&#8221;ye geldi\u011fini varsayal\u0131m. Zar\u0131n \u201c2\u201dye d\u00fc\u015fmesinin deneysel olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>2&#8217;ye gelin<\/em> ) = (2&#8217;ye \u00fc\u00e7 kez gelin) \/ (zarlar\u0131 11 kez at\u0131n) = <strong>3\/11<\/strong><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Fark nas\u0131l hat\u0131rlan\u0131r?<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki hileyi kullanarak teorik olas\u0131l\u0131k ile deneysel olas\u0131l\u0131k aras\u0131ndaki fark\u0131 hat\u0131rlayabilirsiniz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 teorik <strong>olarak<\/strong> matematik kullan\u0131larak hesaplanabilir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir olay\u0131n meydana gelmesinin deneysel olas\u0131l\u0131\u011f\u0131 <strong>, bir deneyin<\/strong> sonu\u00e7lar\u0131n\u0131n do\u011frudan g\u00f6zlemlenmesiyle hesaplanabilir.<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>Teorik olas\u0131l\u0131k kullanman\u0131n avantaj\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u0130statistik\u00e7iler genellikle olaylar\u0131n teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamay\u0131 severler \u00e7\u00fcnk\u00fc hesaplamak ger\u00e7ek bir deney yapmaktan \u00e7ok daha kolay ve h\u0131zl\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, belirli bir okuldaki 30 \u00f6\u011frenciden 1&#8217;inin okuldan sonra matematik \u00f6devlerinde ekstra yard\u0131ma ihtiya\u00e7 duyaca\u011f\u0131n\u0131n bilindi\u011fini varsayal\u0131m. Bir okul y\u00f6neticisi, okul sonras\u0131 ev \u00f6devi yard\u0131m\u0131na ka\u00e7 \u00f6\u011frencinin gelece\u011fini g\u00f6rmek yerine, okuldaki toplam \u00f6\u011frenci say\u0131s\u0131n\u0131 hesaplayabilir (bunun 300 oldu\u011funu varsayal\u0131m) ve bunu teorik olas\u0131l\u0131kla (1\/30) \u00e7arpabilir. Her \u00f6\u011frenciye bireysel olarak yard\u0131m etmek i\u00e7in muhtemelen 10 ki\u015finin bulunmas\u0131 gerekli olacakt\u0131r.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Teorik Olas\u0131l\u0131k \u00d6rnekleri<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Deneysel olas\u0131l\u0131klar\u0131n hesaplanmas\u0131 genellikle teorik olas\u0131l\u0131klardan daha kolayd\u0131r, \u00e7\u00fcnk\u00fc bunlar yaln\u0131zca belirli bir olay\u0131n ger\u00e7ekte ka\u00e7 kez meydana geldi\u011finin toplam deneme say\u0131s\u0131na g\u00f6re say\u0131lmas\u0131n\u0131 i\u00e7erir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Tersine, teorik olas\u0131l\u0131klar\u0131n hesaplanmas\u0131 daha zor olabilir. Konuya hakim olman\u0131za yard\u0131mc\u0131 olacak teorik olas\u0131l\u0131klar\u0131 hesaplaman\u0131n birka\u00e7 \u00f6rne\u011fini burada bulabilirsiniz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00f6rnek 1<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u00e7anta a\u015fa\u011f\u0131daki \u00f6\u011feleri i\u00e7erir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">3 k\u0131rm\u0131z\u0131 top<\/span><\/li>\n<li> <span style=\"color: #000000;\">4 ye\u015fil top<\/span><\/li>\n<li> <span style=\"color: #000000;\">2 mor top<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> G\u00f6zlerinizi kapat\u0131p rastgele bir top al\u0131rsan\u0131z, topun ye\u015fil olma olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Ye\u015fil bir topun kald\u0131r\u0131lma olas\u0131l\u0131\u011f\u0131n\u0131 teorik olarak hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P ( <em>ye\u015fil<\/em> ) = (4 ye\u015fil top) \/ (toplamda 9 top) = <strong>4\/9<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Y\u00fczlerinde 1&#8217;den 9&#8217;a kadar say\u0131lar\u0131n bulundu\u011fu 9 kenarl\u0131 bir zar\u0131n\u0131z var.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> Zar\u0131n sadece bir kez at\u0131lmas\u0131 durumunda zar\u0131n \u201c7\u201d rakam\u0131na gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Zar\u0131n 7&#8217;ye d\u00fc\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 teorik olarak hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P( <em>7&#8217;ye d\u00fc\u015fer<\/em> ) = (zarlar\u0131n 7&#8217;ye d\u00fc\u015fmesi i\u00e7in yaln\u0131zca bir yol vard\u0131r) \/ (9 olas\u0131 taraf) = <strong>1\/9<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 3<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir \u00e7antada 3 erkek ve 7 yedi k\u0131z\u0131n ismi bulunmaktad\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Soru:<\/strong> G\u00f6zlerinizi kapat\u0131p \u00e7antadan rastgele bir isim \u00e7\u0131kar\u0131rsan\u0131z, bir k\u0131z ismini \u00e7\u0131karma olas\u0131l\u0131\u011f\u0131n\u0131z nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Cevap:<\/strong> Bir k\u0131z\u0131n ad\u0131n\u0131 kald\u0131rman\u0131z\u0131n teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P ( <em>k\u0131z isimleri<\/em> ) = (7 olas\u0131 k\u0131z ismi) \/ (toplam 10 isim) = <strong>7\/10<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Olas\u0131l\u0131k, istatistikte belirli olaylar\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 a\u00e7\u0131klayan bir konudur. Olas\u0131l\u0131k hakk\u0131nda konu\u015ftu\u011fumuzda genellikle iki t\u00fcrden birine ba\u015fvururuz: 1. Teorik olas\u0131l\u0131k Teorik olas\u0131l\u0131k, saf matemati\u011fe dayal\u0131 olarak bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r. A olay\u0131n\u0131n meydana gelme teorik olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in form\u00fcl \u015f\u00f6yledir: P( A ) = istenen sonu\u00e7lar\u0131n say\u0131s\u0131 \/ olas\u0131 sonu\u00e7lar\u0131n toplam say\u0131s\u0131 \u00d6rne\u011fin, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-579","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Teorik olas\u0131l\u0131k: tan\u0131m + \u00f6rnekler - Statorials<\/title>\n<meta name=\"description\" content=\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren teorik olas\u0131l\u0131\u011f\u0131n basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/teorik-olasilik\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Teorik olas\u0131l\u0131k: tan\u0131m + \u00f6rnekler - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren teorik olas\u0131l\u0131\u011f\u0131n basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/teorik-olasilik\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T10:51:25+00:00\" \/>\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=\"3 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\/\",\"url\":\"https:\/\/statorials.org\/tr\/teorik-olasilik\/\",\"name\":\"Teorik olas\u0131l\u0131k: tan\u0131m + \u00f6rnekler - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T10:51:25+00:00\",\"dateModified\":\"2023-07-29T10:51:25+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren teorik olas\u0131l\u0131\u011f\u0131n basit bir a\u00e7\u0131klamas\u0131.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/teorik-olasilik\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/teorik-olasilik\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/teorik-olasilik\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teorik olas\u0131l\u0131k: tan\u0131m + \u00f6rnekler\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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