{"id":30,"date":"2023-08-06T13:07:15","date_gmt":"2023-08-06T13:07:15","guid":{"rendered":"https:\/\/statorials.org\/tr\/olaylar-bagimsiz-olaylar\/"},"modified":"2023-08-06T13:07:15","modified_gmt":"2023-08-06T13:07:15","slug":"olaylar-bagimsiz-olaylar","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olaylar-bagimsiz-olaylar\/","title":{"rendered":"Ba\u011f\u0131ms\u0131z olaylar (veya ba\u011f\u0131ms\u0131z olaylar)"},"content":{"rendered":"

Bu yaz\u0131da ba\u011f\u0131ms\u0131z olaylar olarak da adland\u0131r\u0131lan iki ba\u011f\u0131ms\u0131z olay\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ba\u011f\u0131ms\u0131z olay \u00f6rneklerini ve bu t\u00fcr olaylar\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 da bulacaks\u0131n\u0131z. Son olarak ba\u011f\u0131ms\u0131z olaylar ile ba\u011f\u0131ml\u0131 olaylar aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6receksiniz. <\/p>\n

<\/span> Ba\u011f\u0131ms\u0131z olaylar nelerdir?<\/span><\/h2>\n

Ba\u011f\u0131ms\u0131z olaylar, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olmayan rastgele bir deneyin sonu\u00e7lar\u0131d\u0131r<\/strong> . Ba\u015fka bir deyi\u015fle, A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 B olay\u0131n\u0131n meydana gelmesine ba\u011fl\u0131 de\u011filse A ve B olaylar\u0131 ba\u011f\u0131ms\u0131zd\u0131r ve bunun tersi de ge\u00e7erlidir.<\/p>\n

Ba\u011f\u0131ms\u0131z olaylara ba\u011f\u0131ms\u0131z olaylar<\/strong> da denir. <\/p>\n

<\/span> Ba\u011f\u0131ms\u0131z olaylara \u00f6rnekler<\/span><\/h2>\n

Ba\u011f\u0131ms\u0131z olaylar\u0131n (veya ba\u011f\u0131ms\u0131z olaylar\u0131n) tan\u0131m\u0131n\u0131 g\u00f6z \u00f6n\u00fcnde bulundurarak, anlamlar\u0131n\u0131 daha iyi anlamak i\u00e7in \u015fimdi bu t\u00fcr olaylar\u0131n birka\u00e7 \u00f6rne\u011fine bakaca\u011f\u0131z.<\/p>\n

\u00d6rne\u011fin, bir paray\u0131 iki kez att\u0131\u011f\u0131n\u0131zda, “ilk at\u0131\u015fta tura”<\/em> ve “ikinci at\u0131\u015fta tura”<\/em> olaylar\u0131 ba\u011f\u0131ms\u0131zd\u0131r \u00e7\u00fcnk\u00fc ikinci at\u0131\u015fta tura veya yaz\u0131 gelmesi ilk at\u0131\u015f\u0131n sonucuna ba\u011fl\u0131 de\u011fildir. . .<\/p>\n

Ba\u011f\u0131ms\u0131z olaylar\u0131n \u00f6rnekleri, bir kart\u0131n bir desteden iki (veya daha fazla) kez rastgele \u00e7ekilmesinde de bulunabilir. Hangi kart \u00e7ekilirse \u00e7ekilsin, e\u011fer onu desteye geri koyarsak, bu, ikinci \u00e7ekili\u015fte \u015fu veya bu kart\u0131n \u00e7ekilme olas\u0131l\u0131\u011f\u0131n\u0131 etkilemez.<\/p>\n

K\u0131sacas\u0131 ba\u011f\u0131ms\u0131z olaylar, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirinden ba\u011f\u0131ms\u0131z oldu\u011fundan \u00f6nceki olaylardan etkilenmezler<\/strong> . <\/p>\n

<\/span> Ba\u011f\u0131ms\u0131z olaylar\u0131n olas\u0131l\u0131\u011f\u0131<\/span><\/h2>\n

\u0130ki ba\u011f\u0131ms\u0131z olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131,<\/strong> her bir olay\u0131n ayr\u0131 ayr\u0131 meydana gelme olas\u0131l\u0131klar\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fittir.<\/p>\n<\/p>\n

\"P(A\\cap<\/p>\n<\/p>\n

\u00d6rnek olarak, \u201czar at\u0131ld\u0131\u011f\u0131nda 4 rakam\u0131n\u0131n gelmesi\u201d<\/em> ve \u201cpara at\u0131ld\u0131\u011f\u0131nda tura gelmesi\u201d gibi<\/em> ba\u011f\u0131ms\u0131z olaylar\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayaca\u011f\u0131z. Hesaplamay\u0131 yapabilmek i\u00e7in \u00f6nce her olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131 ayr\u0131 ayr\u0131 belirlemeli, sonra bunlar\u0131 \u00e7arpmal\u0131y\u0131z.<\/p>\n

Bir zar att\u0131\u011f\u0131n\u0131zda alt\u0131 olas\u0131 sonu\u00e7 vard\u0131r, yani zar\u0131 att\u0131\u011f\u0131n\u0131zda 4 say\u0131s\u0131n\u0131 atma olas\u0131l\u0131\u011f\u0131:<\/p>\n<\/p>\n

\"P(A)=\\cfrac{1}{6}=0,17\"<\/p>\n<\/p>\n

\u00d6te yandan, yaz\u0131 tura at\u0131ld\u0131\u011f\u0131nda iki olas\u0131 olay vard\u0131r: yaz\u0131 veya tura. Buna g\u00f6re, bir para at\u0131ld\u0131\u011f\u0131nda tura gelme olas\u0131l\u0131\u011f\u0131:<\/p>\n<\/p>\n

\"P(B)=\\cfrac{1}{2}=0,5\"<\/p>\n<\/p>\n

\u0130ki olay ba\u011f\u0131ms\u0131z oldu\u011fundan, her iki olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131, her bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 \u00e7arp\u0131larak hesaplan\u0131r: <\/p>\n<\/p>\n

\"P(A\\cap<\/p>\n<\/p>\n

<\/span> Ba\u011f\u0131ms\u0131z olaylar ve ba\u011f\u0131ml\u0131 olaylar<\/span><\/h2>\n

Ba\u011f\u0131ms\u0131z olaylar ile ba\u011f\u0131ml\u0131 olaylar aras\u0131ndaki fark,<\/strong> ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131na ba\u011f\u0131ml\u0131l\u0131kt\u0131r. Bir olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 di\u011fer olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 etkilemiyorsa iki olay ba\u011f\u0131ms\u0131zd\u0131r. Ancak, bir olay\u0131n olas\u0131l\u0131\u011f\u0131 di\u011fer olay\u0131n ger\u00e7ekle\u015fip ger\u00e7ekle\u015fmemesine ba\u011fl\u0131 oldu\u011funda iki olay ba\u011f\u0131ml\u0131d\u0131r.<\/p>\n

\u00d6rne\u011fin, bir torbaya be\u015f mavi top ve \u00fc\u00e7 turuncu top koyarsak, bir topu \u00e7\u0131kard\u0131\u011f\u0131m\u0131zda onu torbaya geri koyup koymamam\u0131za ba\u011fl\u0131 olarak olaylar birbirinden ba\u011f\u0131ms\u0131z olacak ya da olmayacakt\u0131r.<\/p>\n

Mavi bir top \u00e7ekip torbaya geri koyarsak, tekrar mavi top \u00e7ekme olas\u0131l\u0131\u011f\u0131 \u00f6nceki sonu\u00e7tan etkilenmez ve dolay\u0131s\u0131yla bunlar iki ba\u011f\u0131ms\u0131z olayd\u0131r.<\/p>\n<\/p>\n

\"P(\\text{sacar<\/p>\n<\/p>\n

Tam tersine, mavi bir topu \u00e7\u0131kar\u0131p torbaya koymazsak, torbada art\u0131k daha az mavi top olaca\u011f\u0131 i\u00e7in mavi topun geri gelme olas\u0131l\u0131\u011f\u0131 azal\u0131r. Bu durumda iki ba\u011f\u0131ml\u0131 olay vard\u0131r.<\/p>\n<\/p>\n

\"P(\\text{sacar<\/p>\n<\/p>\n

\u00d6zetle ba\u011f\u0131ms\u0131z olaylar ve ba\u011f\u0131ml\u0131 olaylar, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131n\u0131n hesaplanmas\u0131 i\u00e7in birbirinden ayr\u0131lmas\u0131 gereken iki farkl\u0131 kavramd\u0131r.<\/p>\n","protected":false},"excerpt":{"rendered":"

Bu yaz\u0131da ba\u011f\u0131ms\u0131z olaylar olarak da adland\u0131r\u0131lan iki ba\u011f\u0131ms\u0131z olay\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ba\u011f\u0131ms\u0131z olay \u00f6rneklerini ve bu t\u00fcr olaylar\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 da bulacaks\u0131n\u0131z. Son olarak ba\u011f\u0131ms\u0131z olaylar ile ba\u011f\u0131ml\u0131 olaylar aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6receksiniz. Ba\u011f\u0131ms\u0131z olaylar nelerdir? Ba\u011f\u0131ms\u0131z olaylar, ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olmayan rastgele bir deneyin sonu\u00e7lar\u0131d\u0131r . Ba\u015fka bir […]<\/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-30","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\n\u25b7 Ba\u011f\u0131ms\u0131z olaylar (veya ba\u011f\u0131ms\u0131z olaylar)<\/title>\n<meta name=\"description\" content=\"Ba\u011f\u0131ms\u0131z olaylar (veya ba\u011f\u0131ms\u0131z olaylar) nelerdir, ba\u011f\u0131ms\u0131z olay \u00f6rnekleri ve ba\u011f\u0131ms\u0131z olaylar\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/olaylar-bagimsiz-olaylar\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta 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