<\/p>\n
\u00d6\u011frencilerin s\u0131kl\u0131kla kar\u0131\u015ft\u0131rd\u0131\u011f\u0131 iki terim birbirinden ayr\u0131<\/strong> ve ba\u011f\u0131ms\u0131zd\u0131r<\/strong> .<\/span><\/p>\n \u0130\u015fte birka\u00e7 kelimeyle fark:<\/span><\/p>\n \u0130ki olay ayn\u0131 anda meydana gelmiyorsa ayr\u0131k olaylard\u0131r<\/strong> denir.<\/span><\/p>\n Bir olay\u0131n meydana gelmesinin di\u011fer olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 \u00fczerinde hi\u00e7bir etkisi yoksa iki olaya ba\u011f\u0131ms\u0131z<\/strong> denir.<\/span><\/p>\n A\u015fa\u011f\u0131daki \u00f6rnekler, \u00e7e\u015fitli senaryolarda bu iki terim aras\u0131ndaki fark\u0131 g\u00f6stermektedir.<\/span><\/p>\n Senaryo 1:<\/strong> Yaz\u0131-turay\u0131 bir kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. A olay\u0131n\u0131 paran\u0131n tura d\u00fc\u015fmesi olarak tan\u0131mlarsak ve B olay\u0131n\u0131 paran\u0131n tura d\u00fc\u015fmesi olarak tan\u0131mlarsak, o zaman A olay\u0131 ve B olay\u0131 ayr\u0131kt\u0131r<\/strong> \u00e7\u00fcnk\u00fc para tura ve<\/em> y\u00fczeye d\u00fc\u015femez.<\/span><\/p>\n Senaryo 2<\/strong> : Bir paray\u0131 iki kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. A olay\u0131n\u0131 ilk at\u0131\u015fta paran\u0131n tura gelmesi olarak tan\u0131mlarsak ve B olay\u0131n\u0131 da ikinci at\u0131\u015fta paran\u0131n tura gelmesi olarak tan\u0131mlarsak, o zaman A olay\u0131 ve B olay\u0131 ba\u011f\u0131ms\u0131zd\u0131r<\/strong> \u00e7\u00fcnk\u00fc Tek \u00e7ekili\u015fin sonucu sonucu etkilemez di\u011ferinin.<\/span><\/p>\n Senaryo 1:<\/strong> Bir zar\u0131 bir kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. A olay\u0131n\u0131 zar\u0131n \u00e7ift bir say\u0131ya geldi\u011fi olay ve B olay\u0131n\u0131 da zar\u0131n tek bir say\u0131ya geldi\u011fi olay olarak kabul edersek, o zaman A olay\u0131 ile B olay\u0131 ayr\u0131kt\u0131r<\/strong> \u00e7\u00fcnk\u00fc zarlar bir \u00e7ift say\u0131ya ve<\/em> bir tek say\u0131ya d\u00fc\u015femez ayn\u0131 anda numara.<\/span><\/p>\n Senaryo 2<\/strong> : Bir zar\u0131 iki kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. A olay\u0131n\u0131 zar\u0131n ilk at\u0131\u015fta “5” \u00fczerine d\u00fc\u015fmesi olarak tan\u0131mlarsak ve B olay\u0131n\u0131 da zar\u0131n ikinci at\u0131\u015fta “5” \u00fczerine d\u00fc\u015fmesi olarak tan\u0131mlarsak, o zaman A olay\u0131 ve B olay\u0131 ba\u011f\u0131ms\u0131zd\u0131r<\/strong> \u00e7\u00fcnk\u00fc birin sonucudur zar at\u0131lmas\u0131 di\u011ferinin sonucunu etkilemez.<\/span><\/p>\n Senaryo 1:<\/strong> 52 kartl\u0131k standart desteden bir kart se\u00e7ti\u011fimizi varsayal\u0131m. A olay\u0131n\u0131n kart\u0131n Ma\u00e7a olmas\u0131 olay\u0131 olmas\u0131na ve B olay\u0131n\u0131n kart\u0131n Karo olmas\u0131 olay\u0131 olmas\u0131na izin verirsek, o zaman A olay\u0131 ve B olay\u0131 ayr\u0131kt\u0131r<\/strong> \u00e7\u00fcnk\u00fc kart bir Ma\u00e7a ve<\/em> Karo olamaz. ayn\u0131 zamanda.<\/span><\/p>\n Senaryo 2<\/strong> : Standart 52 kartl\u0131k desteden bir kart\u0131 arka arkaya iki kez se\u00e7ti\u011fimizi ve yerine yenisini koydu\u011fumuzu varsayal\u0131m. A olay\u0131n\u0131 ilk \u00e7ekili\u015fte kart\u0131n ma\u00e7a olmas\u0131 olarak tan\u0131mlarsak ve B olay\u0131n\u0131 ikinci \u00e7ekili\u015fte kart\u0131n ma\u00e7a olmas\u0131 olarak tan\u0131mlarsak, o zaman A olay\u0131 ve B olay\u0131 ba\u011f\u0131ms\u0131zd\u0131r<\/strong> \u00e7\u00fcnk\u00fc bir \u00e7ekili\u015fin sonucu sonucu etkilemez di\u011ferinin.<\/span><\/p>\n Olas\u0131l\u0131ksal g\u00f6sterimle yaz\u0131ld\u0131\u011f\u0131nda, e\u011fer kesi\u015fimleri<\/a> s\u0131f\u0131r ise A ve B olaylar\u0131n\u0131n ayr\u0131k<\/strong> oldu\u011funu s\u00f6yleriz. Bu \u015fu \u015fekilde yaz\u0131labilir:<\/span><\/p>\n \u00d6rne\u011fin bir zar\u0131 bir kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Zar\u0131n \u00e7ift say\u0131ya gelmesi olay\u0131 A olay\u0131, zar\u0131n tek say\u0131ya gelmesi olay\u0131 B olay\u0131 olsun.<\/span><\/p>\n Olaylar i\u00e7in \u00f6rnek uzay\u0131<\/a> \u015fu \u015fekilde tan\u0131mlayabiliriz:<\/span><\/p>\n \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<\/strong> olaylard\u0131r \u00e7\u00fcnk\u00fc her ikisi de ayn\u0131 anda ger\u00e7ekle\u015femez.<\/span><\/p>\n Yani \u015funu yazabiliriz:<\/span><\/p>\n Benzer \u015fekilde, olas\u0131l\u0131ksal g\u00f6sterimle yaz\u0131ld\u0131\u011f\u0131nda, a\u015fa\u011f\u0131daki durum do\u011fruysa A ve B olaylar\u0131n\u0131n ba\u011f\u0131ms\u0131z<\/b> oldu\u011funu s\u00f6yleriz:<\/span><\/p>\n \u00d6rne\u011fin bir zar\u0131 iki kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. A olay\u0131, zar\u0131n ilk at\u0131\u015fta “5” \u00fczerine geldi\u011fi olay olsun ve B olay\u0131 da zar\u0131n ikinci at\u0131\u015fta “5” \u00fczerine geldi\u011fi olay olsun.<\/span><\/p>\n Zar\u0131n yere d\u00fc\u015fmesinin olas\u0131 36 yolunun tamam\u0131n\u0131 yazarsak, 36 senaryodan yaln\u0131zca birinde zar\u0131n her iki seferde de “5” \u00fczerine geldi\u011fini g\u00f6r\u00fcr\u00fcz. O halde P(A\u2229B) = 1\/36 diyebiliriz.<\/span><\/p>\n Ayr\u0131ca zar\u0131n ilk at\u0131\u015fta \u201c5\u201d gelme olas\u0131l\u0131\u011f\u0131n\u0131n P(A) = 1\/6 oldu\u011funu da biliyoruz.<\/span><\/p>\n Ayr\u0131ca zar\u0131n ikinci at\u0131\u015fta \u201c5\u201de gelme olas\u0131l\u0131\u011f\u0131n\u0131n P(B) = 1\/6 oldu\u011funu da biliyoruz.<\/span><\/p>\n Yani \u015funu yazabiliriz:<\/span><\/p>\n Bu denklem do\u011fru oldu\u011fundan, bu senaryoda A olay\u0131 ile B olay\u0131n\u0131n ba\u011f\u0131ms\u0131z<\/strong> oldu\u011funu etkili bir \u015fekilde s\u00f6yleyebiliriz.<\/span><\/p>\n A\u015fa\u011f\u0131daki e\u011fitimler \u00e7e\u015fitli istatistiksel terimler hakk\u0131nda ek bilgi sa\u011flar:<\/span><\/p>\n Ayr\u0131k olaylar nelerdir? (Tan\u0131m ve \u00f6rnekler)<\/a> \u00d6\u011frencilerin s\u0131kl\u0131kla kar\u0131\u015ft\u0131rd\u0131\u011f\u0131 iki terim birbirinden ayr\u0131 ve ba\u011f\u0131ms\u0131zd\u0131r . \u0130\u015fte birka\u00e7 kelimeyle fark: \u0130ki olay ayn\u0131 anda meydana gelmiyorsa ayr\u0131k olaylard\u0131r denir. Bir olay\u0131n meydana gelmesinin di\u011fer olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 \u00fczerinde hi\u00e7bir etkisi yoksa iki olaya ba\u011f\u0131ms\u0131z denir. A\u015fa\u011f\u0131daki \u00f6rnekler, \u00e7e\u015fitli senaryolarda bu iki terim aras\u0131ndaki fark\u0131 g\u00f6stermektedir. \u00d6rnek 1: Yaz\u0131 tura atma […]<\/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-2349","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n \u00d6rnek 1: Yaz\u0131 tura atma<\/strong><\/span><\/h3>\n
\u00d6rnek 2: Bir zar\u0131n at\u0131lmas\u0131<\/strong><\/span><\/h3>\n
\u00d6rnek 3: Kart se\u00e7me<\/strong><\/span><\/h3>\n
Olas\u0131l\u0131k g\u00f6sterimi: ayr\u0131k olaylar veya ba\u011f\u0131ms\u0131z olaylar<\/strong><\/span><\/h3>\n
\n
\n
\n
\n
\n
Ek kaynaklar<\/strong><\/span><\/h3>\n
Kar\u015f\u0131l\u0131kl\u0131 olarak kapsay\u0131c\u0131 veya birbirini d\u0131\u015flayan etkinlikler<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"