{"id":1468,"date":"2023-07-26T06:42:02","date_gmt":"2023-07-26T06:42:02","guid":{"rendered":"https:\/\/statorials.org\/tr\/ayrik-olaylar\/"},"modified":"2023-07-26T06:42:02","modified_gmt":"2023-07-26T06:42:02","slug":"ayrik-olaylar","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ayrik-olaylar\/","title":{"rendered":"Ayr\u0131k olaylar nelerdir? (tan\u0131m ve \u00f6rnekler)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Ayr\u0131k olaylar<\/strong> ayn\u0131 anda meydana gelemeyen olaylard\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Olas\u0131l\u0131ksal g\u00f6sterimle yaz\u0131lan <em>A<\/em> ve <em>B<\/em> olaylar\u0131, e\u011fer <a href=\"https:\/\/statorials.org\/tr\/genel-operasyonlar\/\" target=\"_blank\" rel=\"noopener\">kesi\u015fimleri<\/a> s\u0131f\u0131rsa ayr\u0131kt\u0131r. Bu \u015fu \u015fekilde yaz\u0131labilir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A ve B) = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u2229B) = 0<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, bir desteden rastgele bir kart se\u00e7ti\u011fimizi varsayal\u0131m. A olay\u0131, kart\u0131n ma\u00e7a ya da sinek olmas\u0131 olay\u0131 olsun ve B olay\u0131 da kart\u0131n kupa ya da karo olmas\u0131 olay\u0131 olsun.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Olaylar i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/ornek-uzay-1\/\" target=\"_blank\" rel=\"noopener\">\u00f6rnek uzay\u0131<\/a> \u015fu \u015fekilde tan\u0131mlayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">A = {Ma\u00e7a, Sinek}<\/span><\/li>\n<li> <span style=\"color: #000000;\">B = {Kalp, Elmas}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rneklenen iki alan aras\u0131nda \u00e7ak\u0131\u015fma olmad\u0131\u011f\u0131n\u0131 unutmay\u0131n. Dolay\u0131s\u0131yla A ve B olaylar\u0131 ayr\u0131k olaylard\u0131r \u00e7\u00fcnk\u00fc her ikisi de ayn\u0131 anda ger\u00e7ekle\u015femez.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not:<\/strong> Ayr\u0131k olaylara ayn\u0131 <a href=\"https:\/\/statorials.org\/tr\/karsilikli-olarak-kapsayici-ve-birbirini-dislayan\/\" target=\"_blank\" rel=\"noopener\">zamanda birbirini d\u0131\u015flayan<\/a> olaylar da denir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ayr\u0131k olaylara \u00f6rnekler<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0130\u015fte ayr\u0131k olaylara birka\u00e7 \u00f6rnek daha.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: beraberlik<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Diyelim ki bir yaz\u0131 tura att\u0131n\u0131z. A olay\u0131 paran\u0131n tura geldi\u011fi olay, B olay\u0131 ise paran\u0131n tura geldi\u011fi olay olsun.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131 ve B olay\u0131 ayr\u0131k olacakt\u0131r \u00e7\u00fcnk\u00fc her ikisi de ayn\u0131 anda meydana gelemez. Madeni para yaz\u0131 <em>veya<\/em> tura gelemez.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: zar atma<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Diyelim ki bir zar att\u0131n\u0131z. Zar\u0131n tek say\u0131ya geldi\u011fi olay A olay\u0131, zar\u0131n \u00e7ift say\u0131ya geldi\u011fi olay B olay\u0131 olsun.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131 ve B olay\u0131 ayr\u0131k olacakt\u0131r \u00e7\u00fcnk\u00fc her ikisi de ayn\u0131 anda meydana gelemez. Zar, \u00e7ift say\u0131n\u0131n <em>ve<\/em> tek say\u0131n\u0131n \u00fczerine d\u00fc\u015femez.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 3: Pro Bowl Konumu<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">NFL&#8217;nin Pro Bowl&#8217;a ev sahipli\u011fi yapacak bir yer se\u00e7mek istedi\u011fini varsayal\u0131m. Miami ve San Diego&#8217;daki se\u00e7enekleri daraltt\u0131lar. \u0130ki ismi bir \u015fapkaya yerle\u015ftiriyorlar ve rastgele birini se\u00e7iyorlar. A Etkinli\u011finin Miami&#8217;yi se\u00e7tikleri etkinlik oldu\u011funu ve Etkinlik B&#8217;nin de San Diego&#8217;yu se\u00e7tikleri etkinlik oldu\u011funu varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A olay\u0131 ve B olay\u0131 ayr\u0131k olacakt\u0131r \u00e7\u00fcnk\u00fc her ikisi de ayn\u0131 anda meydana gelemez. Miami ve San Diego&#8217;nun ikisi de se\u00e7ilemez.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ayr\u0131k olaylar\u0131 g\u00f6r\u00fcnt\u00fcle<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Ayr\u0131k olaylar\u0131 g\u00f6rselle\u015ftirmenin yararl\u0131 bir yolu Venn diyagram\u0131 olu\u015fturmakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">E\u011fer iki olay <strong>birbirinden ayr\u0131ysa<\/strong> Venn \u015femas\u0131nda hi\u00e7bir \u015fekilde \u00f6rt\u00fc\u015fmezler:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14541\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/disjoint1.png\" alt=\"Ayr\u0131k olaylar\" width=\"474\" height=\"340\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Tersine, e\u011fer iki olay <strong>birbirinden ayr\u0131 de\u011filse<\/strong> , Venn diyagram\u0131nda en az\u0131ndan bir miktar \u00f6rt\u00fc\u015fme olacakt\u0131r:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14542\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/disjoint2.png\" alt=\"Ayr\u0131k ve ayr\u0131k olmayan olaylar\" width=\"476\" height=\"343\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ayr\u0131k olaylar\u0131n olas\u0131l\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Daha \u00f6nce de belirtildi\u011fi gibi, e\u011fer iki olay birbirinden ayr\u0131ysa, her ikisinin de ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131 s\u0131f\u0131rd\u0131r.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A\u2229B) = 0<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Benzer \u015fekilde, <em>her iki<\/em> olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131, her bir olay\u0131n bireysel olas\u0131l\u0131klar\u0131 toplanarak hesaplanabilir.<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A\u222aB) = P(A) + P(B)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin, A olay\u0131 zar\u0131n 1 veya 2&#8217;ye d\u00fc\u015fmesi olay\u0131 olsun ve B olay\u0131 da zar\u0131n 5 veya 6&#8217;ya d\u00fc\u015fmesi olay\u0131 olsun.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Olaylar i\u00e7in \u00f6rnek uzay\u0131 \u015fu \u015fekilde tan\u0131mlayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">bir = {1, 2}<\/span><\/li>\n<li> <span style=\"color: #000000;\">B = {5, 6}<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A olay\u0131n\u0131n veya B olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 \u015fu \u015fekilde hesaplar\u0131z:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">P(A\u222aB) = P(A) + P(B)<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u222aB) = 2\/6 + 2\/6<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(A\u222aB) = 4\/6 = 2\/3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A olay\u0131n\u0131n <em>veya<\/em> B olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 <strong>2\/3&#8217;t\u00fcr<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimler di\u011fer yayg\u0131n olas\u0131l\u0131k konular\u0131n\u0131n a\u00e7\u0131klamalar\u0131n\u0131 sa\u011flar:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/a-veya-b-olasiligi\/\" target=\"_blank\" rel=\"noopener\">A veya B olas\u0131l\u0131\u011f\u0131 nas\u0131l bulunur: \u00f6rneklerle<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/a-ve-b-olasiligi\/\" target=\"_blank\" rel=\"noopener\">A ve B&#8217;nin Olas\u0131l\u0131\u011f\u0131 Nas\u0131l Bulunur: \u00d6rneklerle<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/toplam-olasilik-yasasi\/\" target=\"_blank\" rel=\"noopener\">Toplam olas\u0131l\u0131k yasas\u0131: tan\u0131m ve \u00f6rnekler<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ayr\u0131k olaylar ayn\u0131 anda meydana gelemeyen olaylard\u0131r. Olas\u0131l\u0131ksal g\u00f6sterimle yaz\u0131lan A ve B olaylar\u0131, e\u011fer kesi\u015fimleri s\u0131f\u0131rsa ayr\u0131kt\u0131r. Bu \u015fu \u015fekilde yaz\u0131labilir: P(A ve B) = 0 P(A\u2229B) = 0 \u00d6rne\u011fin, bir desteden rastgele bir kart se\u00e7ti\u011fimizi varsayal\u0131m. A olay\u0131, kart\u0131n ma\u00e7a ya da sinek olmas\u0131 olay\u0131 olsun ve B olay\u0131 da kart\u0131n kupa ya [&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-1468","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>Ayr\u0131k olaylar nelerdir? 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Daha fazlas\u0131n\u0131 bil","sameAs":["https:\/\/statorials.org\/tr"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/1468","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/comments?post=1468"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/posts\/1468\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/media?parent=1468"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/categories?post=1468"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/tr\/wp-json\/wp\/v2\/tags?post=1468"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}