{"id":35,"date":"2023-08-06T10:52:51","date_gmt":"2023-08-06T10:52:51","guid":{"rendered":"https:\/\/statorials.org\/tr\/etkinliklerle-yapilan-islemler\/"},"modified":"2023-08-06T10:52:51","modified_gmt":"2023-08-06T10:52:51","slug":"etkinliklerle-yapilan-islemler","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/etkinliklerle-yapilan-islemler\/","title":{"rendered":"Etkinliklerle yap\u0131lan i\u015flemler"},"content":{"rendered":"<p>Burada olaylarla hangi i\u015flemlerin yap\u0131labilece\u011fini ve olaylarla yap\u0131lan her i\u015flem t\u00fcr\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca olaylarla yap\u0131lan i\u015flemlere ili\u015fkin ad\u0131m ad\u0131m al\u0131\u015ft\u0131rmalarla pratik yapabilirsiniz.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-operaciones-con-sucesos\"><\/span> Olaylarla i\u015flem t\u00fcrleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Olas\u0131l\u0131k teorisinde olaylarla ilgili \u00fc\u00e7 t\u00fcr i\u015flem vard\u0131r:<\/p>\n<ul>\n<li> <strong><a href=\"https:\/\/statorials.org\/tr\/olaylarin-birlesme-olasiligi\/\">Olaylar\u0131n birli\u011fi<\/a><\/strong> : Bir olay\u0131n veya di\u011ferinin meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li> <strong><a href=\"https:\/\/statorials.org\/tr\">Olaylar\u0131n kesi\u015fmesi<\/a><\/strong> : \u0130ki veya daha fazla olay\u0131n ortak olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<li> <strong>Olay Fark\u0131<\/strong> : Bir olay\u0131n meydana gelmesi ancak ayn\u0131 anda ba\u015fka bir olay\u0131n meydana gelmeme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/li>\n<\/ul>\n<p> Her bir olay operasyonu tipini basit\u00e7e tan\u0131mlayarak, her bir operasyon tipinin nas\u0131l ger\u00e7ekle\u015ftirildi\u011fini anlamak zordur. Bu nedenle a\u015fa\u011f\u0131da \u00fc\u00e7 i\u015flemi daha ayr\u0131nt\u0131l\u0131 olarak a\u00e7\u0131klayaca\u011f\u0131z.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"union-de-sucesos\"><\/span> olaylar\u0131n birli\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A ve B <strong>gibi iki olay\u0131n birle\u015fimi,<\/strong> A olay\u0131n\u0131n, B olay\u0131n\u0131n veya her iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/p>\n<p> \u0130ki farkl\u0131 olay\u0131n birle\u015fiminin simgesi U&#8217;dur, dolay\u0131s\u0131yla iki olay\u0131n birle\u015fimi, olaylar\u0131 temsil eden iki harfin ortas\u0131ndaki U ile ifade 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-f50505c0ff1d2e55a78d3f7ff7f84346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cup B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>\u0130ki olay\u0131n birle\u015fme olas\u0131l\u0131\u011f\u0131,<\/strong> her bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 toplam\u0131 eksi iki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131na e\u015fittir.<\/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-be7c6347c0f331eeb6540ac9e15081dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cup B)=P(A)+P(B)-P(A\\cap B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"299\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00d6rne\u011fin, zar at\u0131ld\u0131\u011f\u0131nda <em>&#8220;\u00e7ift say\u0131 gelme&#8221;<\/em> veya <em>&#8220;4&#8217;ten b\u00fcy\u00fck say\u0131 gelme&#8221;<\/em> olaylar\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayaca\u011f\u0131z.<\/p>\n<p> Zar at\u0131ld\u0131\u011f\u0131nda \u00e7ift say\u0131 elde etmenin \u00fc\u00e7 olas\u0131l\u0131\u011f\u0131 vard\u0131r (2, 4 ve 6), dolay\u0131s\u0131yla olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131:<\/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-507520eabc66126944ccf6869984ce22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\{2,4,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/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-8e7182c80426b8d6d491af6c679f0527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{3}{6}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"124\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> \u00d6te yandan, d\u00f6rtten b\u00fcy\u00fck yaln\u0131zca iki say\u0131 vard\u0131r (5 ve 6), bu nedenle olas\u0131l\u0131klar\u0131:<\/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-141dd1e0fa8df6a6db4ccbb63cc89dd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B=\\{5,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/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-563300d3d19119cf838f3ce63d4bf789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)=\\cfrac{2}{6}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ve iki olay\u0131n kesi\u015fimi her iki olayda da g\u00f6r\u00fcnen say\u0131lara kar\u015f\u0131l\u0131k gelir, yani:<\/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-f0ba40be6117cc3e22d6d347389dea9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cap B=\\{6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/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-65de1160fc1ca0bf26e9acf7f5fd8c9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=\\cfrac{1}{6}=0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"177\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> K\u0131saca A ve B olaylar\u0131n\u0131n birle\u015ftirilmesiyle ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131: <\/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-09c6f02f4584314058aaadd171152410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A\\cup B)&amp; =P(A)+P(B)-P(A\\cap B)\\\\[2ex] &amp; =0,5+0,33-0,167\\\\[2ex] &amp;=0,67\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"299\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interseccion-de-sucesos\"><\/span> olaylar\u0131n kesi\u015fimi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A ve B <strong>olaylar\u0131n\u0131n kesi\u015fimi,<\/strong> A ve B olaylar\u0131n\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r.<\/p>\n<p> \u0130ki olay\u0131n kesi\u015fimini g\u00f6steren sembol ters U ile temsil 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-d142a3ddc9de576e468ef331890da9e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cap B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>\u0130ki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131,<\/strong> her bir olay\u0131n ayr\u0131 ayr\u0131 olas\u0131l\u0131klar\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir.<\/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-593a1a131cab23d805d8324e21e6b4ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=P(A)\\cdot P(B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> A\u00e7\u0131k\u00e7as\u0131, iki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in bu iki olay\u0131n uyumlu olmas\u0131 gerekir. <\/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\/uyumlu-etkinlikler\/\">Hangi etkinlikler uyumludur?<\/a><\/div>\n<p> \u00d6rnek olarak, zar\u0131n at\u0131lmas\u0131 s\u0131ras\u0131nda <em>&#8220;\u00e7ift say\u0131 alma&#8221;<\/em> ve <em>&#8220;4&#8217;ten b\u00fcy\u00fck say\u0131 alma&#8221;<\/em> olaylar\u0131n\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 bulaca\u011f\u0131z.<\/p>\n<p> Yukar\u0131da hesaplad\u0131\u011f\u0131m\u0131z gibi her bir olay\u0131n ayr\u0131 ayr\u0131 ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-3 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-507520eabc66126944ccf6869984ce22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\{2,4,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/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-8e7182c80426b8d6d491af6c679f0527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{3}{6}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"124\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-141dd1e0fa8df6a6db4ccbb63cc89dd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B=\\{5,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/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-563300d3d19119cf838f3ce63d4bf789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)=\\cfrac{2}{6}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Dolay\u0131s\u0131yla iki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131, her bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131 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-467241b200c59905ecdcb42d834bc7ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A\\cap B)&amp; =P(A)\\cdot P(B)\\\\[2ex] &amp; =0,5\\cdot 0,33\\\\[2ex] &amp;=0,167\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"193\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"diferencia-de-sucesos\"><\/span> olaylar\u0131n farkl\u0131l\u0131\u011f\u0131<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A eksi B <strong>iki olay\u0131n\u0131n fark\u0131<\/strong> , A&#8217;n\u0131n B&#8217;de olmayan t\u00fcm temel olaylar\u0131na kar\u015f\u0131l\u0131k gelir. Ba\u015fka bir deyi\u015fle, A eksi B iki olay\u0131n\u0131n fark\u0131nda A olay\u0131 kar\u015f\u0131lan\u0131r, ancak B olay\u0131 ayn\u0131 anda kar\u015f\u0131lanamaz.<\/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-52a50ded14e604d3d89d5df4d87449e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A-B\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"49\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A ve B <strong>olaylar\u0131 aras\u0131ndaki fark olas\u0131l\u0131\u011f\u0131,<\/strong> A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 eksi A ve B taraf\u0131ndan payla\u015f\u0131lan temel olaylar\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131na e\u015fittir.<\/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-6629f4be6b709ade16ee97ae8a42d8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A-B)=P(A)-P(A\\cap B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"237\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u00d6nceki iki i\u015flem t\u00fcr\u00fcnde oldu\u011fu gibi ayn\u0131 \u00f6rne\u011fi takip ederek, bunun ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131, zar at\u0131ld\u0131\u011f\u0131nda <em>&#8220;\u00e7ift say\u0131 elde etme&#8221;<\/em> eksi <em>&#8220;4&#8217;ten b\u00fcy\u00fck say\u0131 elde etme&#8221;<\/em> olay\u0131n\u0131n fark\u0131ndan belirleyece\u011fiz.<\/p>\n<p> A, B olaylar\u0131n\u0131n ve bunlar\u0131n kesi\u015fme olas\u0131l\u0131klar\u0131 a\u015fa\u011f\u0131daki gibidir (yukar\u0131da ayr\u0131nt\u0131l\u0131 hesaplamay\u0131 g\u00f6rebilirsiniz): <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-507520eabc66126944ccf6869984ce22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\{2,4,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\"><\/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-8e7182c80426b8d6d491af6c679f0527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A)=\\cfrac{3}{6}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"124\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-141dd1e0fa8df6a6db4ccbb63cc89dd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B=\\{5,6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/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-563300d3d19119cf838f3ce63d4bf789_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(B)=\\cfrac{2}{6}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"135\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-632af7dc98e8dfe1d290dad299b7ed8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\\cap B= \\{6\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\"><\/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-5534b4bfc1a446e367ee89c8b92a210e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(A\\cap B)=\\cfrac{1}{6}= 0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"177\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<p> Bu nedenle iki olay aras\u0131ndaki fark\u0131n ortaya \u00e7\u0131kma 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-e7aed40cdbbe256ec9b19c670f1d7607_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A-B)&amp;=P(A)-P(A\\cap B)\\\\[2ex] &amp; =0,5-0,167\\\\[2ex] &amp; =0,33\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"237\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Merak konusu olarak AB olaylar\u0131n\u0131n farkl\u0131l\u0131\u011f\u0131 ayn\u0131 zamanda A olay\u0131 ile B olay\u0131n\u0131n tamamlay\u0131c\u0131 (veya z\u0131tt\u0131) olay\u0131n\u0131n kesi\u015fimine e\u015fde\u011fer olma \u00f6zelli\u011fine de sahiptir. <\/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-ef7d6b43d04514a954789f1ca5ef085d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A-B=A\\cap\\overline{B}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"121\" style=\"vertical-align: 0px;\"><\/p>\n<\/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\/zit-olay-tamamlayici-olay\/\">Tamamlay\u0131c\u0131 olay nedir?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-operaciones-con-sucesos\"><\/span> Olaylarla i\u015flemlere ili\u015fkin \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> 1. Egzersiz<\/h3>\n<p> Alt\u0131 y\u00fczl\u00fc bir zar at\u0131ld\u0131\u011f\u0131nda tek say\u0131 gelme veya 3&#8217;ten k\u00fc\u00e7\u00fck say\u0131 gelme olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00e7\u00f6z\u00fcm\u00fc g\u00f6r<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Bu al\u0131\u015ft\u0131rmada \u015fu veya bu olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamal\u0131y\u0131z, dolay\u0131s\u0131yla iki olay\u0131n birle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 bulmal\u0131y\u0131z.<\/p>\n<p class=\"has-text-align-left\"> Bu nedenle ilk \u00f6nce Laplace yasas\u0131n\u0131 uygulayarak tek say\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 hesapl\u0131yoruz:<\/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-979ad7431176d3876eefe36603c62fb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{n\\'umero impar})=\\cfrac{3}{6}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0130kinci olarak 3&#8217;ten k\u00fc\u00e7\u00fck bir say\u0131 alma olas\u0131l\u0131\u011f\u0131n\u0131 belirliyoruz:<\/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-f5bbf47b98e14d8d013618a4febadd1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{n\\'umero menor que 3})=\\cfrac{2}{6}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"281\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u015eimdi olaylarda tekrar eden temel olaylar\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayal\u0131m ki bu sadece 1 say\u0131s\u0131d\u0131r (yaln\u0131zca tek say\u0131 3&#8217;ten k\u00fc\u00e7\u00fckt\u00fcr):<\/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-def5fea23c1336469a00fb1d7f8a1c9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{n\\'umero impar y menor que 3})=\\cfrac{1}{6}=0,167\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"356\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ve son olarak, olas\u0131l\u0131klar\u0131n\u0131 bulmak i\u00e7in iki olay\u0131n birle\u015fimi form\u00fcl\u00fcn\u00fc uyguluyoruz: <\/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-09c6f02f4584314058aaadd171152410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A\\cup B)&amp; =P(A)+P(B)-P(A\\cap B)\\\\[2ex] &amp; =0,5+0,33-0,167\\\\[2ex] &amp;=0,67\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"299\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Al\u0131\u015ft\u0131rma 2<\/h3>\n<p> Bir kutuya 3 turuncu, 2 mavi ve 5 beyaz top koyuyoruz. Bir topu al\u0131p kutuya geri koymak ve ard\u0131ndan ba\u015fka bir topu \u00e7\u0131karmak gibi rastgele bir deney yap\u0131yoruz. Birinci topun mavi, ikincinin turuncu top \u00e7ekme olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00e7\u00f6z\u00fcm\u00fc g\u00f6r<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Bu sorunu \u00e7\u00f6zmek i\u00e7in iki olay\u0131n kesi\u015fimini hesaplamal\u0131y\u0131z \u00e7\u00fcnk\u00fc her iki temel olay\u0131n da do\u011fru olmas\u0131n\u0131 istiyoruz.<\/p>\n<p class=\"has-text-align-left\"> Bu nedenle ilk olarak Laplace kural\u0131n\u0131 uygulayarak mavi topun yakalanma olas\u0131l\u0131\u011f\u0131n\u0131 hesapl\u0131yoruz:<\/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-2115f0ea9c6fe50a8dab8d498b4ef634_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{sacar bola azul})=\\cfrac{2}{3+2+5}=0,2\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"287\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Daha sonra turuncu bir top elde etme olas\u0131l\u0131\u011f\u0131n\u0131 buluyoruz:<\/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-edba4b58924cad3279e8aef1c629e272_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{sacar bola naranja})=\\cfrac{3}{3+2+5}=0,3\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"316\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Ve son olarak, bulunan iki olas\u0131l\u0131\u011f\u0131 \u00e7arparak iki olay\u0131n kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesapl\u0131yoruz:<\/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-cfcbe0cbee264116460aa623fe22b8f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P(A\\cap B)&amp; =P(A)\\cdot P(B)\\\\[2ex] &amp; =0,2\\cdot 0,3\\\\[2ex] &amp;=0,06\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"193\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sonu\u00e7 olarak, ilk denemede mavi topu, ikinci denemede turuncu topu yakalama \u015fans\u0131 yaln\u0131zca %6&#8217;d\u0131r.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Al\u0131\u015ft\u0131rma 3<\/h3>\n<p> Marta&#8217;n\u0131n bir s\u0131nav\u0131 ge\u00e7me olas\u0131l\u0131\u011f\u0131 1\/3, Juan&#8217;\u0131n da ayn\u0131 s\u0131nav\u0131 ge\u00e7me olas\u0131l\u0131\u011f\u0131 2\/5&#8217;tir. Marta&#8217;n\u0131n ba\u015far\u0131l\u0131, Juan&#8217;\u0131n ise ba\u015far\u0131s\u0131z olma olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__FFF8E1\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#FFF8E1\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u00e7\u00f6z\u00fcm\u00fc g\u00f6r<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Bu al\u0131\u015ft\u0131rmada iki olay aras\u0131ndaki fark\u0131 hesaplamam\u0131z gerekiyor \u00e7\u00fcnk\u00fc Marta&#8217;n\u0131n onaylamas\u0131n\u0131 istiyoruz ama Juan&#8217;\u0131n onaylamamas\u0131n\u0131 istiyoruz. Bunu yapmak i\u00e7in, olaylarla bu t\u00fcr i\u015flemlere y\u00f6nelik form\u00fcl\u00fc kullanman\u0131z yeterlidir:<\/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-d0e95b0b85a9436f42caf8eaa44f2a38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}\\displaystyle A-B =A\\cap\\overline{B}=\\\\[2ex]\\displaystyle =\\frac{1}{3}\\cdot \\left(1-\\frac{2}{5}\\right) = \\frac{1}{3} \\cdot \\frac{3}{5}=\\\\[3ex] =\\cfrac{3}{15} = 0,2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"134\" width=\"194\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Marta&#8217;n\u0131n ba\u015far\u0131l\u0131 olmas\u0131 ve Juan&#8217;\u0131n ayn\u0131 anda ba\u015far\u0131s\u0131z olmas\u0131 olas\u0131l\u0131\u011f\u0131 bu nedenle %20&#8217;dir.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Burada olaylarla hangi i\u015flemlerin yap\u0131labilece\u011fini ve olaylarla yap\u0131lan her i\u015flem t\u00fcr\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca olaylarla yap\u0131lan i\u015flemlere ili\u015fkin ad\u0131m ad\u0131m al\u0131\u015ft\u0131rmalarla pratik yapabilirsiniz. Olaylarla i\u015flem t\u00fcrleri Olas\u0131l\u0131k teorisinde olaylarla ilgili \u00fc\u00e7 t\u00fcr i\u015flem vard\u0131r: Olaylar\u0131n birli\u011fi : Bir olay\u0131n veya di\u011ferinin meydana gelme olas\u0131l\u0131\u011f\u0131d\u0131r. Olaylar\u0131n kesi\u015fmesi : \u0130ki veya daha fazla olay\u0131n ortak olas\u0131l\u0131\u011f\u0131d\u0131r. [&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-35","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 Olaylarla i\u015flemler: birle\u015fim, kesi\u015fim ve fark<\/title>\n<meta name=\"description\" content=\"\u0130\u015flemleri olaylarla ve her i\u015flem t\u00fcr\u00fcn\u00fcn nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. 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