{"id":24,"date":"2023-08-06T16:31:59","date_gmt":"2023-08-06T16:31:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/olay-bilesik-olay\/"},"modified":"2023-08-06T16:31:59","modified_gmt":"2023-08-06T16:31:59","slug":"olay-bilesik-olay","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/olay-bilesik-olay\/","title":{"rendered":"Bile\u015fik olay (veya bile\u015fik olay)"},"content":{"rendered":"

Bu yaz\u0131da bile\u015fik olay olarak da adland\u0131r\u0131lan bile\u015fik olay\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Bile\u015fik olaylar\u0131n \u00f6rneklerini ve bile\u015fik olay\u0131n basit bir olaydan ne kadar farkl\u0131 oldu\u011funu bulacaks\u0131n\u0131z. Son olarak bu t\u00fcr olaylar aras\u0131nda yap\u0131labilecek i\u015flemleri g\u00f6rebileceksiniz.<\/p>\n

<\/span> Bile\u015fik olay nedir?<\/span><\/h2>\n

Bile\u015fik olay olarak da adland\u0131r\u0131lan bile\u015fik olay<\/strong> ,<\/strong> rastgele bir deneyin olas\u0131 sonu\u00e7lar\u0131n\u0131n bir k\u00fcmesidir.<\/p>\n

Bu nedenle bile\u015fik olay, basit olaylar\u0131n<\/strong> bir k\u00fcmesi ve \u00f6rnek uzay\u0131n<\/strong> bir alt k\u00fcmesidir. <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> \u00d6rnek uzay nedir?<\/a><\/div>\n

<\/span> Bile\u015fik Olay \u00d6rnekleri<\/span><\/h2>\n

Bile\u015fik olay\u0131n (veya bile\u015fik olay\u0131n) tan\u0131m\u0131n\u0131 g\u00f6z \u00f6n\u00fcnde bulundurarak a\u015fa\u011f\u0131da bu t\u00fcr olaylar\u0131n birka\u00e7 \u00f6rne\u011fini a\u00e7\u0131klayaca\u011f\u0131z. Bu b\u00f6l\u00fcm\u00fcn amac\u0131 bile\u015fik olay\u0131n anlam\u0131n\u0131 anlaman\u0131zd\u0131r, dolay\u0131s\u0131yla bu konuda sorular\u0131n\u0131z varsa yorumlarda bize sorabilirsiniz.<\/p>\n

Bile\u015fik olaylar\u0131n \u00e7e\u015fitli \u00f6rnekleri, zar\u0131n tek bir at\u0131\u015f\u0131yla tan\u0131mlanabilir. \u00d6rne\u011fin, \u00e7ift say\u0131n\u0131n yuvarlanmas\u0131 bile\u015fik bir olayd\u0131r \u00e7\u00fcnk\u00fc \u00fc\u00e7 olas\u0131 sonu\u00e7 s\u00f6z konusudur: 2, 4 ve 6 say\u0131lar\u0131.<\/p>\n

\u0130ki madeni paray\u0131 havaya atarken de bile\u015fik olaylar\u0131 g\u00f6zlemleyebiliriz. Art arda iki at\u0131\u015fta madalyonun ayn\u0131 y\u00fcz\u00fcn\u00fcn al\u0131nmas\u0131, hem olay (tura, yaz\u0131) hem de olay (tura, yaz\u0131) olabilece\u011finden bile\u015fik bir olayd\u0131r.<\/p>\n

<\/span> bile\u015fik olay ve basit olay<\/span><\/h2>\n

Daha sonra bile\u015fik olay ile basit olay aras\u0131ndaki fark\u0131<\/strong> a\u00e7\u0131klayaca\u011f\u0131z \u00e7\u00fcnk\u00fc bunlar temel olmas\u0131na ra\u011fmen s\u0131kl\u0131kla kar\u0131\u015ft\u0131r\u0131lan iki farkl\u0131 kavramd\u0131r.<\/p>\n

Basit bir olay (veya basit olay), rastgele bir deneyin tek bir sonucudur; bile\u015fik olay (veya bile\u015fik olay), iki veya daha fazla olas\u0131 sonu\u00e7tan olu\u015fan bir dizidir. Ba\u015fka bir deyi\u015fle bile\u015fik olay, basit olaylar\u0131n birle\u015fimidir.<\/p>\n

\u00d6rne\u011fin kal\u0131p haddeleme deneyinde 1 numaral\u0131 y\u00fcz\u00fcn elde edilmesi basit bir olayd\u0131r. \u00d6te yandan 6’dan k\u00fc\u00e7\u00fck bir say\u0131n\u0131n yuvarlanmas\u0131 be\u015f basit olaydan (1, 2, 3, 4 ve 5) olu\u015fan bir olayd\u0131r.<\/p>\n

Bu durumda, olaylar e\u015fit olas\u0131l\u0131kl\u0131 oldu\u011fundan, tek bir olay\u0131n olas\u0131l\u0131\u011f\u0131, birini olas\u0131 sonu\u00e7lar\u0131n toplam say\u0131s\u0131na b\u00f6lerek kolayca belirlenebilir:<\/p>\n<\/p>\n

\"P=\\cfrac{1}{6}=0,1667<\/p>\n<\/p>\n

Bile\u015fik olay\u0131n olas\u0131l\u0131\u011f\u0131,<\/strong> olumlu durumlar\u0131n toplam say\u0131s\u0131n\u0131n olas\u0131 sonu\u00e7lar\u0131n toplam say\u0131s\u0131na b\u00f6l\u00fcnmesiyle hesaplan\u0131r. \u00d6rne\u011fin, bir zar\u0131n at\u0131lmas\u0131 s\u0131ras\u0131nda 6’dan k\u00fc\u00e7\u00fck bir say\u0131n\u0131n at\u0131lmas\u0131 \u015feklindeki bile\u015fik durumda, be\u015f uygun durum vard\u0131r, dolay\u0131s\u0131yla ortaya \u00e7\u0131kma olas\u0131l\u0131\u011f\u0131 5\/6’d\u0131r.<\/p>\n<\/p>\n

\"P=\\cfrac{5}{6}=0,8333<\/p>\n<\/p>\n

Olas\u0131l\u0131k teorisinde bu form\u00fcle Laplace kural\u0131 denir.<\/p>\n

A\u015fa\u011f\u0131daki ba\u011flant\u0131da basit olaylara ili\u015fkin daha fazla \u00f6rnek g\u00f6rebilirsiniz: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> basit olay \u00f6rnekleri <\/div>\n

<\/span> Bile\u015fik olaylarla i\u015flemler<\/span><\/h2>\n

Bile\u015fik olaylarla a\u015fa\u011f\u0131daki i\u015flemler ger\u00e7ekle\u015ftirilebilir:<\/p>\n

    \n
  • Bile\u015fik olaylar\u0131n birle\u015fimi<\/strong> : A ve B gibi iki farkl\u0131 olay\u0131n (veya olay\u0131n) birle\u015fimi, A’n\u0131n olay k\u00fcmesi art\u0131 B’nin olay k\u00fcmesinin toplam\u0131na e\u015fittir.<\/li>\n<\/ul>\n

    \u00d6rne\u011fin, A bile\u015fik olay\u0131 {1,3,4} say\u0131lar\u0131na ve B bile\u015fi\u011fi olay\u0131 {2, 4} say\u0131lar\u0131na kar\u015f\u0131l\u0131k geliyorsa, iki olay\u0131n birle\u015fimi {1, 2, 3, 4 k\u00fcmesi olacakt\u0131r. }.<\/p>\n<\/p>\n

    \"\\left.\\begin{array}{l}A=\\{1,3,4\\}\\\\[2ex]B=\\{2,4\\}<\/p>\n<\/p>\n

      \n
    • Bile\u015fik olaylar\u0131n kesi\u015fimi<\/strong> : \u0130ki bile\u015fik olay\u0131n kesi\u015fmesi yaln\u0131zca her iki k\u00fcmeye ait olan olaylarla ilgilidir.<\/li>\n<\/ul>\n

      A bile\u015fik olay\u0131 {1,3,4} say\u0131lar\u0131ndan ve B bile\u015fi\u011fi olay\u0131 {2, 4} say\u0131lar\u0131ndan olu\u015fuyorsa iki olay\u0131n kesi\u015fimi yaln\u0131zca 4 say\u0131s\u0131 olacakt\u0131r.<\/p>\n<\/p>\n

      \"\\left.\\begin{array}{l}A=\\{1,3,4\\}\\\\[2ex]B=\\{2,4\\}<\/p>\n<\/p>\n

        \n
      • Bile\u015fik olaylar\u0131n fark\u0131<\/strong> : A eksi B olmak \u00fczere iki olay\u0131n fark\u0131, A’y\u0131 do\u011frulayan ve B’yi do\u011frulayan olaylara e\u015fittir.<\/li>\n<\/ul>\n

        \u00d6rne\u011fin, bile\u015fik olay A, {1,3,4} say\u0131lar\u0131na ve bile\u015fik olay B, {2, 4} say\u0131lar\u0131na kar\u015f\u0131l\u0131k geliyorsa, A olay\u0131 eksi B olay\u0131 aras\u0131ndaki fark {1,3} olur.<\/p>\n<\/p>\n

        \"\\left.\\begin{array}{l}A=\\{1,3,4\\}\\\\[2ex]B=\\{2,4\\}<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

        Bu yaz\u0131da bile\u015fik olay olarak da adland\u0131r\u0131lan bile\u015fik olay\u0131n ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. Bile\u015fik olaylar\u0131n \u00f6rneklerini ve bile\u015fik olay\u0131n basit bir olaydan ne kadar farkl\u0131 oldu\u011funu bulacaks\u0131n\u0131z. Son olarak bu t\u00fcr olaylar aras\u0131nda yap\u0131labilecek i\u015flemleri g\u00f6rebileceksiniz. Bile\u015fik olay nedir? Bile\u015fik olay olarak da adland\u0131r\u0131lan bile\u015fik olay , rastgele bir deneyin olas\u0131 sonu\u00e7lar\u0131n\u0131n bir k\u00fcmesidir. Bu nedenle […]<\/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-24","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\nBile\u015fik olay (veya bile\u015fik olay): tan\u0131m ve \u00f6rnekler<\/title>\n<meta name=\"description\" content=\"Bile\u015fik olay\u0131n (veya bile\u015fik olay\u0131n) ne oldu\u011funu a\u00e7\u0131kl\u0131yoruz. 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