A. TANIM Olas\u0131l\u0131k, sonucu kesin olmayan olaylarla ilgilenir. Bir zar at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze gelen noktalar\u0131n say\u0131s\u0131n\u0131n ne olaca\u011f\u0131 gibi \u015fans oyunlar\u0131yla ilgilenen olas\u0131l\u0131k teorisi g\u00fcn\u00fcm\u00fczde sosyal olaylar ve bilimsel \u00e7al\u0131\u015fmalarda da kullan\u0131lmaktad\u0131r.<\/p>\n
B. OLASILIK TER\u0130MLER\u0130
\n Bir madeni para havaya at\u0131ld\u0131\u011f\u0131nda yaz\u0131 m\u0131 ya da tura m\u0131 gelece\u011fini (v.b) tesbit etme i\u015flemine deney denir.
\n Bir deneyin her bir g\u00f6r\u00fcnt\u00fcs\u00fcne (\u00e7\u0131kt\u0131s\u0131na) sonu\u00e7 denir.
\n Bir deneyin b\u00fct\u00fcn sonu\u00e7lar\u0131n\u0131 eleman kabul eden k\u00fcmeye \u00f6rnek uzay ve \u00f6rnek uzay\u0131n her bir eleman\u0131na \u00f6rnek nokta denir.
\n Bir \u00f6rnek uzay\u0131n her bir alt k\u00fcmesine olay denir.
\n \u00d6rnek uzay\u0131n alt k\u00fcmelerinden olan bo\u015f k\u00fcmeye imkans\u0131z (olanaks\u0131z) olay denir.
\n \u00d6rnek uzay\u0131n b\u00fct\u00fcn elemanlar\u0131n\u0131 i\u00e7eren alt k\u00fcmesine mutlak (kesin) olay denir.
\nA ve B, E \u00f6rnek uzay\u0131na ait iki olay olsun.
\nA \u00c7 B = \u00c6
\nise, A ve B olay\u0131na ayr\u0131k olay denir.<\/p>\n
C. OLASILIK FONKS\u0130YONU
\n E \u00f6rnek uzay\u0131n\u0131n b\u00fct\u00fcn alt k\u00fcmelerinin olu\u015fturdu\u011fu kuvvet k\u00fcmesi K olsun.
\n P : K \u00ae [0, 1]
\n bi\u00e7iminde tan\u0131mlanan P fonksiyonuna olas\u0131l\u0131k fonksiyonu denir. A \u00ce K ise P(A) ger\u00e7el say\u0131s\u0131na A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 denir.
\n\u00dc1) Her A \u00ce K i\u00e7in, 0 \u00a3 P(A) \u00a3 1 dir. Yani, A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 0 ile 1 aras\u0131ndad\u0131r.
\n2) \u0130mkans\u0131z olay\u0131n olas\u0131l\u0131\u011f\u0131 0 ve kesin olay\u0131n olas\u0131l\u0131\u011f\u0131 1 dir.
\n3) A, B \u00ce K ve A \u00c7 B = \u00c6 ise,
\n P(A \u00c8 B) = P(A) + P(B) dir.
\n\u00dc 1) 2) A \u00cc B ise P(A) \u00a3 P(B) dir.
\n3) A, A n\u0131n t\u00fcmleyeni olmak \u00fczere,
\n P(A) + P(\u2013A) = 1 dir.
\n4) P(A \u00c8 B) = P(A) + P(B) \u2013 P(A \u00c7 B)
\n5) A, B, C olaylar\u0131 E \u00f6rnek uzay\u0131n\u0131n iki\u015fer iki\u015fer ayr\u0131k b\u00fct\u00fcn olaylar\u0131 ise,
\n (E = A \u00c8 B \u00c8 C)
\n P(A) + P(B) + P(C) = 1 dir.
\n\u00dc 1) n, paran\u0131n at\u0131lma say\u0131s\u0131n\u0131 veya para say\u0131s\u0131n\u0131 g\u00f6stermek \u00fczere, \u00f6rnek uzay 2n
\n dir.
\n\u00dc 2) n, zar\u0131n at\u0131lma say\u0131s\u0131n\u0131 veya zar say\u0131s\u0131n\u0131 g\u00f6stermek \u00fczere, \u00f6rnek uzay 6n dir.<\/p>\n
D. BA\u011eIMSIZ VE BA\u011eIMLI OLAYLAR
\n Bir olay\u0131n elde edilmesi, di\u011fer olay\u0131n elde edilmesini etkilemiyorsa bu iki olaya ba\u011f\u0131ms\u0131z olaylar denir.
\n E\u011fer iki olay ba\u011f\u0131ms\u0131z de\u011fil ise, bu olaylara birbirine ba\u011f\u0131ml\u0131d\u0131r denir.
\n\u00dc A ve B ba\u011f\u0131ms\u0131z iki olay olsun. A n\u0131n ve B nin ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 :
\n P(A \u00c7 B) = P(A) . P(B) dir.<\/p>\n
E. KO\u015eULLU OLASILIK
\n A ve B, E \u00f6rnek uzay\u0131nda iki olay olsun. B olay\u0131n\u0131n ger\u00e7ekle\u015fmi\u015f olmas\u0131 durumunda, A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131na, A olay\u0131n\u0131n B ye ba\u011fl\u0131 ko\u015fullu olas\u0131l\u0131\u011f\u0131 denir ve P(A \\ B) ile g\u00f6sterilir.<\/p>\n
Bir deneyde bir A olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 x olsun. Bu deney n kez tekrarland\u0131\u011f\u0131nda A olay\u0131n\u0131n k kez ger\u00e7ekle\u015fmesi olas\u0131l\u0131\u011f\u0131,<\/p>\n","protected":false},"excerpt":{"rendered":"
A. TANIM Olas\u0131l\u0131k, sonucu kesin olmayan olaylarla ilgilenir. Bir zar at\u0131ld\u0131\u011f\u0131nda \u00fcst y\u00fcze gelen noktalar\u0131n say\u0131s\u0131n\u0131n ne olaca\u011f\u0131 gibi \u015fans oyunlar\u0131yla ilgilenen olas\u0131l\u0131k teorisi g\u00fcn\u00fcm\u00fczde sosyal olaylar ve bilimsel \u00e7al\u0131\u015fmalarda da kullan\u0131lmaktad\u0131r. B. OLASILIK TER\u0130MLER\u0130 Bir madeni para havaya at\u0131ld\u0131\u011f\u0131nda yaz\u0131 m\u0131 ya da tura m\u0131 gelece\u011fini (v.b) tesbit etme i\u015flemine deney denir. Bir deneyin …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[3543,1929],"class_list":["post-3128","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-alt-kume","tag-olasilik"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3128"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3128\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}