{"id":1019,"date":"2023-07-27T23:33:02","date_gmt":"2023-07-27T23:33:02","guid":{"rendered":"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/"},"modified":"2023-07-27T23:33:02","modified_gmt":"2023-07-27T23:33:02","slug":"carpma-isleminin-genel-kurali","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/","title":{"rendered":"\u00c7arpman\u0131n genel kural\u0131 (a\u00e7\u0131klama ve \u00f6rnekler)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Genel \u00e7arpma kural\u0131,<\/strong> herhangi iki olay\u0131n (A ve B) her ikisinin de meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n \u015fu \u015fekilde hesaplanabilece\u011fini belirtir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(A ve B) = P(A) * P(B|A)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Dikey \u00e7ubuk | &#8220;verilen&#8221; anlam\u0131na gelir. Dolay\u0131s\u0131yla P(B|A), &#8220;A&#8217;n\u0131n meydana geldi\u011fi <em>g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda<\/em> , B&#8217;nin meydana gelme olas\u0131l\u0131\u011f\u0131&#8221; olarak okunabilir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A ve B olaylar\u0131 ba\u011f\u0131ms\u0131zsa, P(B|A) basit\u00e7e P(B)&#8217;ye e\u015fittir ve kural a\u015fa\u011f\u0131daki gibi basitle\u015ftirilebilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>P(A ve B) = P(A) * P(B)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu genel \u00e7arpma kural\u0131n\u0131 pratikte nas\u0131l uygulayabilece\u011fimizi g\u00f6rmek i\u00e7in baz\u0131 ba\u011f\u0131ms\u0131z ve ba\u011f\u0131ml\u0131 olay \u00f6rneklerini g\u00f6zden ge\u00e7irelim.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ml\u0131 olaylar i\u00e7in genel \u00e7arpma kural\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, iki ba\u011f\u0131ml\u0131 olayla ilgili olas\u0131l\u0131klar\u0131 bulmak i\u00e7in genel \u00e7arpma kural\u0131n\u0131n nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir. Her \u00f6rnekte, ikinci olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131, birinci olay\u0131n sonucundan etkilenir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: bir kavanozdaki toplar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir kavanozda 4 k\u0131rm\u0131z\u0131 ve 3 ye\u015fil top bulunmaktad\u0131r. Bob torbadan rastgele 2 topu geri koymadan se\u00e7ecek. 2 k\u0131rm\u0131z\u0131 top se\u00e7me olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> \u0130lk denemede k\u0131rm\u0131z\u0131 top se\u00e7me olas\u0131l\u0131\u011f\u0131 4\/7&#8217;dir. Bu top kald\u0131r\u0131ld\u0131\u011f\u0131nda ikinci denemede k\u0131rm\u0131z\u0131 top se\u00e7me olas\u0131l\u0131\u011f\u0131 3\/6&#8217;d\u0131r. Yani 2 k\u0131rm\u0131z\u0131 top se\u00e7me olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P (her ikisi de k\u0131rm\u0131z\u0131) = 4\/7 * 3\/7 \u2248 <strong>0,2249<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: destedeki kartlar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir iskambil destesinde 26 siyah ve 26 k\u0131rm\u0131z\u0131 kart bulunmaktad\u0131r. Debbie, desteden rastgele 2 kart\u0131 de\u011fi\u015ftirmeden se\u00e7ecektir. 2 k\u0131rm\u0131z\u0131 kart se\u00e7me olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> \u0130lk denemede k\u0131rm\u0131z\u0131 kart se\u00e7me olas\u0131l\u0131\u011f\u0131 26\/52&#8217;dir. Bu kart kald\u0131r\u0131ld\u0131\u011f\u0131nda ikinci denemede k\u0131rm\u0131z\u0131 kart se\u00e7me olas\u0131l\u0131\u011f\u0131 25\/51&#8217;dir. Yani 2 k\u0131rm\u0131z\u0131 kart se\u00e7me olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P (her ikisi de k\u0131rm\u0131z\u0131) = 26\/52 * 25\/51 \u2248 <strong>0,2451<\/strong><\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ba\u011f\u0131ms\u0131z olaylar i\u00e7in genel \u00e7arpma kural\u0131<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler, iki ba\u011f\u0131ms\u0131z olayla ilgili olas\u0131l\u0131klar\u0131 bulmak i\u00e7in genel \u00e7arpma kural\u0131n\u0131n nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir. Her \u00f6rnekte, ikinci olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131, birinci olay\u0131n sonucundan <em>etkilenmemektedir<\/em> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: iki madeni para atmak<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Diyelim ki iki para \u00e7ekti\u011fimizi varsayal\u0131m. \u0130ki paran\u0131n tura gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> \u0130lk paran\u0131n tura gelme olas\u0131l\u0131\u011f\u0131 1\/2&#8217;dir. \u0130lk paran\u0131n hangi tarafa geldi\u011fine bak\u0131lmaks\u0131z\u0131n ikinci paran\u0131n tura gelme olas\u0131l\u0131\u011f\u0131 da 1\/2&#8217;dir. B\u00f6ylece iki paran\u0131n tura gelme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P (her ikisi de tura d\u00fc\u015fer) = 1\/2 * 1\/2 = <strong>0,25<\/strong><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: \u0130ki zar at\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Diyelim ki ayn\u0131 anda iki zar at\u0131yoruz. Her iki zar\u0131n da 1 numaraya gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7\u00f6z\u00fcm:<\/strong> \u0130lk zar\u0131n \u201c1\u201de gelme olas\u0131l\u0131\u011f\u0131 1\/6\u2019d\u0131r. \u0130lk zar\u0131n hangi tarafa geldi\u011fine bak\u0131lmaks\u0131z\u0131n ikinci zar\u0131n \u201c1\u201de gelme olas\u0131l\u0131\u011f\u0131 da 1\/6&#8217;d\u0131r. Yani her iki zar\u0131n da &#8220;1&#8221;e gelme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplanabilir:<\/span><\/p>\n<p> <span style=\"color: #000000;\">P(Her ikisi de \u201c1\u201de iner) = 1\/6 * 1\/6 = 1\/36 \u2248 <strong>0,0278<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Genel \u00e7arpma kural\u0131, herhangi iki olay\u0131n (A ve B) her ikisinin de meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131n \u015fu \u015fekilde hesaplanabilece\u011fini belirtir: P(A ve B) = P(A) * P(B|A) Dikey \u00e7ubuk | &#8220;verilen&#8221; anlam\u0131na gelir. Dolay\u0131s\u0131yla P(B|A), &#8220;A&#8217;n\u0131n meydana geldi\u011fi g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda , B&#8217;nin meydana gelme olas\u0131l\u0131\u011f\u0131&#8221; olarak okunabilir. A ve B olaylar\u0131 ba\u011f\u0131ms\u0131zsa, P(B|A) basit\u00e7e P(B)&#8217;ye [&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-1019","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>\u00c7arpman\u0131n genel kural\u0131 (a\u00e7\u0131klama ve \u00f6rnekler)<\/title>\n<meta name=\"description\" content=\"Bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere genel \u00e7arpma kural\u0131n\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\/carpma-isleminin-genel-kurali\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00c7arpman\u0131n genel kural\u0131 (a\u00e7\u0131klama ve \u00f6rnekler)\" \/>\n<meta property=\"og:description\" content=\"Bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere genel \u00e7arpma kural\u0131n\u0131n basit bir a\u00e7\u0131klamas\u0131.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T23:33:02+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\/carpma-isleminin-genel-kurali\/\",\"url\":\"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/\",\"name\":\"\u00c7arpman\u0131n genel kural\u0131 (a\u00e7\u0131klama ve \u00f6rnekler)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-27T23:33:02+00:00\",\"dateModified\":\"2023-07-27T23:33:02+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bir tan\u0131m ve \u00e7e\u015fitli \u00f6rnekler de dahil olmak \u00fczere genel \u00e7arpma kural\u0131n\u0131n basit bir a\u00e7\u0131klamas\u0131.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/carpma-isleminin-genel-kurali\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"\u00c7arpman\u0131n genel kural\u0131 (a\u00e7\u0131klama ve \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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