{"id":147,"date":"2023-08-04T23:11:18","date_gmt":"2023-08-04T23:11:18","guid":{"rendered":"https:\/\/statorials.org\/tr\/agac-diyagrami\/"},"modified":"2023-08-04T23:11:18","modified_gmt":"2023-08-04T23:11:18","slug":"agac-diyagrami","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/agac-diyagrami\/","title":{"rendered":"A\u011fa\u00e7 diyagram\u0131"},"content":{"rendered":"<p>Bu makalede a\u011fa\u00e7 diyagram\u0131n\u0131n ne oldu\u011fu ve nas\u0131l yap\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece a\u011fa\u00e7 yap\u0131lar\u0131n\u0131n \u00f6rneklerini, bu t\u00fcr diyagram\u0131n avantajlar\u0131n\u0131 ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-diagrama-de-arbol\"><\/span> A\u011fa\u00e7 nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Olas\u0131l\u0131k a\u011fac\u0131<\/strong> olarak da adland\u0131r\u0131lan <strong>a\u011fa\u00e7 diyagram\u0131<\/strong> , bir deneyin t\u00fcm olas\u0131 sonu\u00e7lar\u0131n\u0131n olas\u0131l\u0131klar\u0131yla birlikte grafiksel bir temsilidir.<\/p>\n<p> Bu nedenle, bir \u00f6rnek uzaydaki t\u00fcm olas\u0131 sonu\u00e7lar\u0131n grafi\u011fini \u00e7izmek ve olas\u0131l\u0131klar\u0131n\u0131 hesaplamak i\u00e7in bir a\u011fa\u00e7 diyagram\u0131 kullan\u0131l\u0131r.<\/p>\n<p> Bir a\u011fa\u00e7 diyagram\u0131, nihai sonu\u00e7lara ula\u015f\u0131lana kadar her sonucun ( <strong>d\u00fc\u011f\u00fcm<\/strong> ) yeni olas\u0131 sonu\u00e7lara ( <strong>dallara<\/strong> ) dallanaca\u011f\u0131 \u015fekilde yap\u0131l\u0131r. <\/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\/diagramme-en-arbre.png\" alt=\"\" class=\"wp-image-3125\" width=\"341\" height=\"385\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Bir d\u00fc\u011f\u00fcmden \u00e7\u0131kan t\u00fcm dallar\u0131n olas\u0131l\u0131klar\u0131n\u0131n toplam\u0131n\u0131n 1&#8217;e e\u015fit olmas\u0131 gerekti\u011fi unutulmamal\u0131d\u0131r. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-un-diagrama-de-arbol\"><\/span> A\u011fa\u00e7 diyagram\u0131 nas\u0131l yap\u0131l\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Bir a\u011fa\u00e7 olu\u015fturmak<\/strong> i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 izlemelisiniz:<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">A\u011fa\u00e7 diyagram\u0131 olu\u015fturman\u0131n ilk ad\u0131m\u0131 her olas\u0131 sonu\u00e7 i\u00e7in bir dal \u00e7izmektir. Bunlar ilk nesil \u015fubeler olacak.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Daha sonra her bir olaya ili\u015fkin olas\u0131l\u0131k ilgili dal\u0131na eklenir.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Her birinci nesil dal\u0131n sonu, sonraki olas\u0131 olaylar\u0131n dallar\u0131n\u0131n temsil edilmesi gereken bir d\u00fc\u011f\u00fcmd\u00fcr.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">\u0130lk dallarda oldu\u011fu gibi temsil edilen olaylar\u0131n olas\u0131l\u0131klar\u0131n\u0131 eklemeliyiz.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">Son d\u00fc\u011f\u00fcmlere, yani deneyin olas\u0131 sonlar\u0131na ula\u015fana kadar 3. ve 4. ad\u0131mlar\u0131 tekrarlay\u0131n.<\/span><\/li>\n<\/ol>\n<p> Bir seviyedeki \u015fube say\u0131s\u0131n\u0131n mutlaka farkl\u0131 bir seviyedeki \u015fube say\u0131s\u0131na e\u015fit olmas\u0131 gerekmedi\u011fini unutmay\u0131n. Ayn\u0131 \u015fekilde olas\u0131 bir sonucun ortaya \u00e7\u0131kard\u0131\u011f\u0131 dal say\u0131s\u0131 da ayn\u0131 d\u00fczeyde bile de\u011fi\u015fiklik g\u00f6sterebilmektedir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-diagrama-de-arbol\"><\/span> A\u011fa\u00e7 \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k a\u011fa\u00e7 diyagram\u0131 olu\u015fturman\u0131n tan\u0131m\u0131n\u0131 ve teorisini bildi\u011fimize g\u00f6re, kavram\u0131 daha iyi anlamak i\u00e7in ger\u00e7ek d\u00fcnyadan bir \u00f6rne\u011fe ad\u0131m ad\u0131m bakal\u0131m.<\/p>\n<ul>\n<li> \u00dc\u00e7 ba\u011f\u0131ms\u0131z paran\u0131n yaz\u0131 tura at\u0131lmas\u0131n\u0131n olas\u0131l\u0131k a\u011fac\u0131n\u0131 olu\u015fturun. Daha sonra \u00fc\u00e7 at\u0131\u015fta da tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirleyin.<\/li>\n<\/ul>\n<p> Kura \u00e7ekerken yaln\u0131zca iki olas\u0131 sonu\u00e7 vard\u0131r; tura veya yaz\u0131 gelebilir. Buna g\u00f6re, bir para at\u0131ld\u0131\u011f\u0131nda yaz\u0131 veya tura 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-24700638f62e83613a39f2b566e2fb9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara})=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" style=\"vertical-align: -12px;\"><\/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-1bc45ea1827985f95c0e3199c9bc2bdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cruz})=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"143\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Olas\u0131 sonu\u00e7lar\u0131n olas\u0131l\u0131klar\u0131n\u0131 bildi\u011fimizde a\u011fa\u00e7 diyagram\u0131n\u0131 temsil etmeye devam ederiz.<\/p>\n<p> Yaz\u0131-tura at\u0131\u015flar\u0131 ba\u011f\u0131ms\u0131z oldu\u011fundan, yaz\u0131 veya tura gelme olas\u0131l\u0131\u011f\u0131 her at\u0131\u015fta her zaman ayn\u0131 olacakt\u0131r. Bu nedenle a\u011fac\u0131 olu\u015fturmak i\u00e7in, yap\u0131lan her at\u0131\u015fta iki dal\u0131n (ba\u015f ve kuyruk) ayn\u0131 olas\u0131l\u0131kla temsil edilmesi gerekir. <\/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-darbre-diagramme-lancer-trois-pieces.png\" alt=\"a\u011fa\u00e7 diyagram\u0131 \u00f6rne\u011fi, \u00fc\u00e7 yaz\u0131 tura atma\" class=\"wp-image-3130\" width=\"434\" height=\"326\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Ve a\u011fac\u0131 olu\u015fturdu\u011fumuzda tek yapmam\u0131z gereken \u00fc\u00e7 yaz\u0131 tura atman\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek. <\/p>\n<div style=\"background:linear-gradient(to bottom, #FFFFFF 0%, #FFE0B2 100%); padding-top: 23px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px dashed #FF9B28; border-radius:20px;\">\n<p style=\"text-align:left\"> <strong>Bir a\u011fa\u00e7 diyagram\u0131n\u0131n olas\u0131 bir sonucunun olas\u0131l\u0131\u011f\u0131n\u0131 hesaplamak<\/strong> i\u00e7in t\u00fcm biti\u015fik dallar\u0131n olas\u0131l\u0131klar\u0131 \u00e7arp\u0131lmal\u0131d\u0131r.<\/p>\n<\/div>\n<p> Dolay\u0131s\u0131yla bu durumda tura gelme olas\u0131l\u0131klar\u0131n\u0131n t\u00fcm\u00fcn\u00fc \u00e7arpmam\u0131z gerekir \u00e7\u00fcnk\u00fc bunlar bizi istenen sonuca g\u00f6t\u00fcren yolun olas\u0131l\u0131klar\u0131d\u0131r. <\/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\/diagramme-arborescent-calcul-de-probabilite.png\" alt=\"a\u011fa\u00e7 diyagram\u0131, olas\u0131l\u0131k hesaplamas\u0131\" class=\"wp-image-3135\" width=\"436\" height=\"364\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> B\u00f6ylece, \u00fc\u00e7 yaz\u0131 tura at\u0131\u015f\u0131nda tura gelme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\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-b5937bbc6c52680555865995cde7c785_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{cara-cara-cara})=0,5\\cdot 0,5\\cdot 0,5=0,125\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> K\u0131sacas\u0131 art arda \u00fc\u00e7 kez tura gelme olas\u0131l\u0131\u011f\u0131 %12,5&#8217;tir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-diagrama-de-arbol\"><\/span> \u00c7\u00f6z\u00fclm\u00fc\u015f a\u011fa\u00e7 egzersizi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Bir k\u00f6yde sadece 3 kre\u015f bulunmaktad\u0131r; \u00e7ocuklar\u0131n %60&#8217;\u0131 A kre\u015fine, %30&#8217;u B kre\u015fine ve %10&#8217;u C kre\u015fine gitmektedir. Ayr\u0131ca \u00fc\u00e7 kre\u015fte de n\u00fcfusun %55&#8217;i k\u0131zd\u0131r. A\u011fac\u0131 olu\u015fturun ve a\u015fa\u011f\u0131daki olas\u0131l\u0131klar\u0131 hesaplay\u0131n:<\/p>\n<ul>\n<li> Rastgele se\u00e7ilen bir \u00e7ocu\u011fun B kre\u015finden bir k\u0131z olma olas\u0131l\u0131\u011f\u0131.<\/li>\n<li> Herhangi bir kre\u015ften rastgele se\u00e7ilen bir \u00e7ocu\u011fun erkek olma olas\u0131l\u0131\u011f\u0131. <\/li>\n<\/ul>\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>\u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> T\u00fcm kre\u015flerdeki k\u0131zlar\u0131n oran\u0131 %55 ise, erkek \u00e7ocuklar\u0131n y\u00fczdesi basit\u00e7e 1 eksi 0,55 \u00e7\u0131kar\u0131larak hesaplan\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-d6c48cfc81fd4e8283d9366bced38a6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico})=1-0,55=0,45\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"213\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Art\u0131k t\u00fcm olas\u0131l\u0131klar\u0131 bildi\u011fimize g\u00f6re t\u00fcm olas\u0131l\u0131klar\u0131 i\u00e7eren olas\u0131l\u0131k a\u011fac\u0131n\u0131 olu\u015fturabiliriz: <\/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\/exercice-resolu-du-diagramme-arborescent.png\" alt=\"\u00c7\u00f6z\u00fclm\u00fc\u015f a\u011fa\u00e7 egzersizi\" class=\"wp-image-3140\" width=\"312\" height=\"330\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p class=\"has-text-align-left\"> B\u00f6ylece, B kre\u015finden bir k\u0131z\u0131n rastgele se\u00e7ilme olas\u0131l\u0131\u011f\u0131 \u015fu \u015fekilde hesaplan\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-8da69823ee95f9d3eb866b8830c69459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chica guarder\\'ia B})=0,30\\cdot 0,55=\\bm{0,165}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u00d6te yandan, herhangi bir kre\u015fe erkek \u00e7ocuk se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in \u00f6nce her kre\u015fe bir erkek \u00e7ocuk se\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 bulmal\u0131, sonra bunlar\u0131 toplamal\u0131y\u0131z: <\/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-cba123bdad65bc0ef13fe011d12c16e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia A})=0,6\\cdot 0,45=0,27\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"320\" 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-502aba9717f579b47d3aae94af910f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia B})=0,30\\cdot 0,45=0,135\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" 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-4ab8a01b04f94bda577564f835167d88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia C})=0,10\\cdot 0,45=0,045\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"336\" 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-f2e92f117cfeb16530b9f37c647fe4f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(\\text{chico guarder\\'ia A, B o C})=0,27+0,135+0,045=\\bm{0,45}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"467\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ventajas-del-diagrama-de-arbol\"><\/span> A\u011fa\u00e7 yap\u0131s\u0131n\u0131n avantajlar\u0131<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A\u011fa\u00e7 yap\u0131s\u0131n\u0131n \u00f6zelliklerinden dolay\u0131 bu t\u00fcr istatistiksel grafi\u011fin avantajlar\u0131 \u015funlard\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">A\u011fa\u00e7 diyagramlar\u0131 karar vermede \u00e7ok faydal\u0131d\u0131r.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">T\u00fcm olas\u0131 sonu\u00e7lar aras\u0131ndaki ili\u015fki grafiksel olarak g\u00f6sterilebilir.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Bir sorunun temel nedenini bulmak \u00e7ok uygundur.<\/span><\/li>\n<li style=\"margin-bottom:15px\"> <span style=\"color:#101010;font-weight: normal;\">Olas\u0131l\u0131k ve istatistik problemlerini \u00e7\u00f6zmeyi kolayla\u015ft\u0131r\u0131r.<\/span><\/li>\n<li> <span style=\"color:#101010;font-weight: normal;\">A\u011fa\u00e7 diyagram\u0131 fikirleri organize etmeye ve durumu analiz etmeye yard\u0131mc\u0131 olur.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede a\u011fa\u00e7 diyagram\u0131n\u0131n ne oldu\u011fu ve nas\u0131l yap\u0131ld\u0131\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r. B\u00f6ylece a\u011fa\u00e7 yap\u0131lar\u0131n\u0131n \u00f6rneklerini, bu t\u00fcr diyagram\u0131n avantajlar\u0131n\u0131 ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. A\u011fa\u00e7 nedir? Olas\u0131l\u0131k a\u011fac\u0131 olarak da adland\u0131r\u0131lan a\u011fa\u00e7 diyagram\u0131 , bir deneyin t\u00fcm olas\u0131 sonu\u00e7lar\u0131n\u0131n olas\u0131l\u0131klar\u0131yla birlikte grafiksel bir temsilidir. Bu nedenle, bir \u00f6rnek uzaydaki t\u00fcm olas\u0131 sonu\u00e7lar\u0131n grafi\u011fini [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-147","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 A\u011fa\u00e7tan a\u011faca: nas\u0131l yap\u0131l\u0131r, \u00f6rnekler, avantajlar...<\/title>\n<meta name=\"description\" content=\"Burada a\u011fac\u0131n ne oldu\u011funu, a\u011fac\u0131n nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131, a\u011fa\u00e7 \u00f6rneklerini ve avantajlar\u0131n\u0131 ke\u015ffedeceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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