{"id":37,"date":"2023-08-06T09:33:38","date_gmt":"2023-08-06T09:33:38","guid":{"rendered":"https:\/\/statorials.org\/tr\/bilesik-olasilik\/"},"modified":"2023-08-06T09:33:38","modified_gmt":"2023-08-06T09:33:38","slug":"bilesik-olasilik","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/bilesik-olasilik\/","title":{"rendered":"Bile\u015fik olas\u0131l\u0131k"},"content":{"rendered":"<p>Bu yaz\u0131m\u0131zda ortak olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ortak olas\u0131l\u0131k \u00f6rnekleri ve ortak olas\u0131l\u0131k, marjinal olas\u0131l\u0131k ve ko\u015fullu olas\u0131l\u0131k aras\u0131ndaki farklar\u0131n neler oldu\u011funu da bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-probabilidad-conjunta\"><\/span> Ortak olas\u0131l\u0131k nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ortak olas\u0131l\u0131k,<\/strong> iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr.<\/p>\n<p> Olas\u0131l\u0131k kombinasyonu 0 ile 1 aras\u0131nda bir say\u0131d\u0131r. Olas\u0131l\u0131k kombinasyonu ne kadar b\u00fcy\u00fck olursa, olaylar\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131 o kadar y\u00fcksek olur; bunun tersine, olas\u0131l\u0131k, olas\u0131l\u0131k kombinasyonundan b\u00fcy\u00fckse, olaylar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 o kadar d\u00fc\u015f\u00fck olur. olaylar\u0131n ayn\u0131 anda ger\u00e7ekle\u015fmesidir. zamanlar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-probabilidad-conjunta\"><\/span> Ortak olas\u0131l\u0131k form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A ve B olaylar\u0131n\u0131n ortak olas\u0131l\u0131\u011f\u0131, A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 ile B olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir.<\/strong><\/p>\n<p> Bu nedenle, iki farkl\u0131 olay\u0131n ortak olas\u0131l\u0131\u011f\u0131n\u0131 hesaplama form\u00fcl\u00fc \u015f\u00f6yledir:<\/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> Dolay\u0131s\u0131yla iki farkl\u0131 olay\u0131n ortak olas\u0131l\u0131\u011f\u0131, bu olaylar\u0131n kesi\u015fimine e\u015fde\u011ferdir. Ancak \u015funu unutmamal\u0131s\u0131n\u0131z ki bu form\u00fcl\u00fc yaln\u0131zca iki <a href=\"https:\/\/statorials.org\/tr\/olaylar-bagimsiz-olaylar\/\">ba\u011f\u0131ms\u0131z olay<\/a> olmas\u0131 durumunda kullanabilirsiniz, aksi takdirde <a href=\"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/\">ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fcn\u00fc<\/a> kullanman\u0131z gerekir.<\/p>\n<p> Ayr\u0131ca iki olay\u0131n ortak olas\u0131l\u0131\u011f\u0131, her olay\u0131n ayr\u0131 ayr\u0131 meydana gelme olas\u0131l\u0131\u011f\u0131ndan her zaman daha az olacakt\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-probabilidad-conjunta\"><\/span> Ortak Olas\u0131l\u0131k \u00d6rnekleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ortak olas\u0131l\u0131\u011f\u0131n tan\u0131m\u0131n\u0131 g\u00f6z \u00f6n\u00fcnde bulundurarak, anlam\u0131n\u0131 daha iyi anlaman\u0131z i\u00e7in \u015fimdi bu olas\u0131l\u0131k t\u00fcr\u00fcne iki \u00f6rnek a\u00e7\u0131klayaca\u011f\u0131z.<\/p>\n<h3 class=\"wp-block-heading\"> Bir yaz\u0131 tura at\u0131n ve bir zar at\u0131n<\/h3>\n<p> \u00d6rne\u011fin, para at\u0131ld\u0131\u011f\u0131nda tura gelme olas\u0131l\u0131\u011f\u0131 1\/2, zar at\u0131ld\u0131\u011f\u0131nda ise 4 gelme olas\u0131l\u0131\u011f\u0131 1\/6&#8217;d\u0131r. Bu nedenle, tura gelme olas\u0131l\u0131\u011f\u0131 ile 4 say\u0131s\u0131n\u0131n ortak 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-fcbb87b4ec4d1525d162ea0499e6f632_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(A\\cap B)=P(A)\\cdot P(B)=\\\\[2ex] =\\cfrac{1}{2}\\cdot \\cfrac{1}{6}=\\cfrac{1}{12}=0,083\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"77\" width=\"212\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> \u0130ki zar atma etkinli\u011fi<\/h3>\n<p> Ayn\u0131 rastgele deneyde iki farkl\u0131 olay\u0131n ortak olas\u0131l\u0131\u011f\u0131n\u0131 da bulabiliriz. \u00d6rnek olarak, bir zar\u0131n at\u0131lmas\u0131 s\u0131ras\u0131nda <em>\u201ctek say\u0131n\u0131n gelmesi\u201d<\/em> ve <em>\u201c4&#8217;ten b\u00fcy\u00fck bir say\u0131n\u0131n gelmesi\u201d<\/em> olaylar\u0131n\u0131n birlikte ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayaca\u011f\u0131z.<\/p>\n<p> Bir zar\u0131n \u00fczerinde \u00fc\u00e7 tek say\u0131 vard\u0131r (1, 3 ve 5), dolay\u0131s\u0131yla tek say\u0131 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-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, zarda d\u00f6rtten b\u00fcy\u00fck iki say\u0131 vard\u0131r (5 ve 6), dolay\u0131s\u0131yla ikinci olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 \u015f\u00f6yle 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-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> Bu nedenle, iki olay\u0131n ortak olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in bulunan iki olas\u0131l\u0131\u011f\u0131 \u00e7arpman\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-f06dbe6207ae2ea038fe6727f383b5f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}P(A\\cap B)=P(A)\\cdot P(B)=\\\\[2ex] =0,5\\cdot 0,33=0,167\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"212\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-conjunta-y-probabilidad-marginal\"><\/span> Ortak olas\u0131l\u0131k ve marjinal olas\u0131l\u0131k<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ortak olas\u0131l\u0131k ile marjinal olas\u0131l\u0131k aras\u0131ndaki fark<\/strong> , ortak olas\u0131l\u0131\u011f\u0131n iki veya daha fazla olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 ifade etmesi, marjinal olas\u0131l\u0131\u011f\u0131n ise toplam\u0131n bir alt k\u00fcmesinin meydana gelme olas\u0131l\u0131\u011f\u0131 olmas\u0131d\u0131r.<\/p>\n<p> Bir deney yapt\u0131\u011f\u0131m\u0131z\u0131 ve ard\u0131 ard\u0131na 21 g\u00fcn boyunca sabah g\u00fcn\u00fcn g\u00fcne\u015fli mi yoksa bulutlu mu oldu\u011funu, \u00f6\u011fleden sonra ise ya\u011fmur ya\u011f\u0131p ya\u011fmad\u0131\u011f\u0131n\u0131 kaydetti\u011fimizi d\u00fc\u015f\u00fcn\u00fcn: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-probabilite-jointe-et-marginale.png\" alt=\"ortak olas\u0131l\u0131k \u00f6rne\u011fi\" class=\"wp-image-595\" width=\"321\" height=\"155\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \u00d6rne\u011fin, bir g\u00fcn\u00fcn bulutlu olmas\u0131n\u0131n marjinal 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-f4ff1a041ddd1850f21133f0ebfe8a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{nublado})=\\cfrac{11}{21}=0,52\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"190\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ve bir g\u00fcn ya\u011fmur ya\u011fmas\u0131n\u0131n marjinal 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-bfe2f34568b77377b1c870c37a027fe6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{llueve})=\\cfrac{9}{21}=0,43\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"174\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ancak bir g\u00fcn\u00fcn bulutlu ve ya\u011fmurlu olmas\u0131n\u0131n ortak 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-a1f8a535c55fd3d92b114f7767b359fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{nublado y llueve})=\\cfrac{7}{21}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"256\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"probabilidad-conjunta-y-probabilidad-condicional\"><\/span> Ortak olas\u0131l\u0131k ve ko\u015fullu olas\u0131l\u0131k<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> S\u0131kl\u0131kla kar\u0131\u015ft\u0131r\u0131lan di\u011fer iki kavram ortak olas\u0131l\u0131k ve ko\u015fullu olas\u0131l\u0131kt\u0131r, ancak bunlar farkl\u0131 anlamlara gelir.<\/p>\n<p> <strong>Ortak olas\u0131l\u0131k ile ko\u015fullu olas\u0131l\u0131k aras\u0131ndaki fark<\/strong> , ortak olas\u0131l\u0131kta her iki olay\u0131n da ayn\u0131 anda meydana gelmesi gerekti\u011fidir; ko\u015fullu olas\u0131l\u0131k ise bir olay\u0131n ba\u015fka bir olay meydana geldi\u011finde meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 ifade eder. zaten \u00fcretildi. <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-probabilite-jointe-et-marginale.png\" alt=\"ortak ve ko\u015fullu olas\u0131l\u0131k \u00f6rne\u011fi\" class=\"wp-image-595\" width=\"321\" height=\"155\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Ayn\u0131 al\u0131\u015ft\u0131rmay\u0131 daha \u00f6nce tekrarlad\u0131\u011f\u0131m\u0131zda, bir g\u00fcn\u00fcn bulutlu ve ya\u011fmurlu olmas\u0131n\u0131n ortak olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde olur:<\/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-a1f8a535c55fd3d92b114f7767b359fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{nublado y llueve})=\\cfrac{7}{21}=0,33\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"256\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ancak bir g\u00fcn\u00fcn bulutlu oldu\u011fu g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, o g\u00fcn\u00fcn ya\u011fmur ya\u011fmas\u0131 ko\u015fullu (veya ko\u015fullu) 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-8481ae94675947936a45242e56c45365_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" P(\\text{llueve }|\\text{ nublado})=\\cfrac{7}{11}=0,64\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"252\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ko\u015fullu olas\u0131l\u0131k durumunda, o g\u00fcn\u00fcn bulutlu oldu\u011fu bilinerek ya\u011fmur ya\u011fma olas\u0131l\u0131\u011f\u0131 hesaplan\u0131r.<\/p>\n<p> G\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi ko\u015fullu olas\u0131l\u0131k iki olay aras\u0131ndaki dikey \u00e7izgiyle ifade ediliyor.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu yaz\u0131m\u0131zda ortak olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ortak olas\u0131l\u0131k \u00f6rnekleri ve ortak olas\u0131l\u0131k, marjinal olas\u0131l\u0131k ve ko\u015fullu olas\u0131l\u0131k aras\u0131ndaki farklar\u0131n neler oldu\u011funu da bulacaks\u0131n\u0131z. Ortak olas\u0131l\u0131k nedir? Ortak olas\u0131l\u0131k, iki olay\u0131n ayn\u0131 anda meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcmd\u00fcr. Olas\u0131l\u0131k kombinasyonu 0 ile 1 aras\u0131nda bir say\u0131d\u0131r. Olas\u0131l\u0131k kombinasyonu ne [&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-37","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 Ortak olas\u0131l\u0131k: tan\u0131m, form\u00fcl ve \u00f6rnekler<\/title>\n<meta name=\"description\" content=\"Ortak olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 (form\u00fcl) a\u00e7\u0131kl\u0131yoruz. 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