{"id":39,"date":"2023-08-06T08:15:33","date_gmt":"2023-08-06T08:15:33","guid":{"rendered":"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/"},"modified":"2023-08-06T08:15:33","modified_gmt":"2023-08-06T08:15:33","slug":"kosullu-kosullu-olasilik","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/","title":{"rendered":"Ko\u015fullu olas\u0131l\u0131k (veya ko\u015fullu olas\u0131l\u0131k)"},"content":{"rendered":"

Burada ko\u015fullu olas\u0131l\u0131\u011f\u0131n (veya ko\u015fullu olas\u0131l\u0131\u011f\u0131n) ne oldu\u011funu \u00f6\u011freneceksiniz. Ko\u015fullu olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve bu olas\u0131l\u0131k t\u00fcr\u00fcn\u00fcn \u00f6zelliklerini bir \u00f6rnekle a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen ko\u015fullu olas\u0131l\u0131k al\u0131\u015ft\u0131rmalar\u0131 ile pratik yapabileceksiniz. <\/p>\n

<\/span> Ko\u015fullu olas\u0131l\u0131k nedir?<\/span><\/h2>\n

Ko\u015fullu olas\u0131l\u0131k<\/strong> , ayn\u0131 zamanda ko\u015fullu olas\u0131l\u0131k<\/strong> olarak da adland\u0131r\u0131l\u0131r, ba\u015fka bir B olay\u0131n\u0131n meydana gelmesi durumunda A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 g\u00f6steren istatistiksel bir \u00f6l\u00e7\u00fcd\u00fcr. Yani ko\u015fullu olas\u0131l\u0131k P(A|B), A olay\u0131n\u0131n B olay\u0131 ger\u00e7ekle\u015ftikten sonra meydana gelme olas\u0131l\u0131\u011f\u0131n\u0131 ifade eder.<\/p>\n

Ko\u015fullu olas\u0131l\u0131k, iki olay aras\u0131nda dikey bir \u00e7ubukla yaz\u0131l\u0131r: P(A|B) ve \u015funu okur: “B olay\u0131 verildi\u011finde A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131”.<\/p>\n

Ko\u015fullu olas\u0131l\u0131k de\u011ferinin 0 ile 1 aras\u0131nda bir say\u0131 oldu\u011funa dikkat edin. Ko\u015fullu olas\u0131l\u0131k ne kadar y\u00fcksek olursa, B olay\u0131 meydana geldi\u011finde A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 da o kadar y\u00fcksek olur, ancak ko\u015fullu olas\u0131l\u0131k ne kadar d\u00fc\u015f\u00fck olursa, A olay\u0131n\u0131n ger\u00e7ekle\u015fme olas\u0131l\u0131\u011f\u0131 da o kadar d\u00fc\u015f\u00fck olur. B olay\u0131 ger\u00e7ekle\u015fti\u011finde ger\u00e7ekle\u015fecektir. <\/p>\n

<\/span> Ko\u015fullu Olas\u0131l\u0131k Form\u00fcl\u00fc<\/span><\/h2>\n

Belirli bir B olay\u0131n\u0131n A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131,<\/strong> A olay\u0131 ile B olay\u0131 aras\u0131ndaki kesi\u015fme olas\u0131l\u0131\u011f\u0131n\u0131n B olay\u0131n\u0131n olas\u0131l\u0131\u011f\u0131na b\u00f6l\u00fcnmesine e\u015fittir. <\/p>\n

\"ko\u015fullu<\/figure>\n

Ko\u015fullu olas\u0131l\u0131k (veya ko\u015fullu olas\u0131l\u0131k) form\u00fcl\u00fcn\u00fcn yaln\u0131zca ko\u015fulsuz olay\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131 s\u0131f\u0131r de\u011filse, yani P(B)\u22600 ise kullan\u0131labilece\u011fini unutmay\u0131n. Veya ba\u015fka bir deyi\u015fle B olay\u0131n\u0131n ger\u00e7ekle\u015fmesi m\u00fcmk\u00fcn ise.<\/p>\n

Ko\u015fullu olas\u0131l\u0131k bunun tersinden de hesaplanabilir, yani P(B|A) biliniyorsa P(A|B) belirlenebilir. Ancak bunu yapmak i\u00e7in Bayes teoremini uygulaman\u0131z gerekir; bu teoremin nelerden olu\u015ftu\u011funu burada g\u00f6rebilirsiniz: <\/p>\n

\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> Bayes teoremi nedir? <\/div>\n

<\/span> Ko\u015fullu Olas\u0131l\u0131k \u00d6rne\u011fi<\/span><\/h2>\n

Ko\u015fullu olas\u0131l\u0131\u011f\u0131n tan\u0131m\u0131 ve form\u00fcl\u00fcn\u00fcn ne oldu\u011funu g\u00f6rd\u00fckten sonra, anlam\u0131n\u0131 tam olarak anlamak i\u00e7in bu t\u00fcr olas\u0131l\u0131klar\u0131n bir \u00f6rne\u011fini ad\u0131m ad\u0131m \u00e7\u00f6zece\u011fiz.<\/p>\n

    \n
  • 30 ki\u015filik bir s\u0131n\u0131fta s\u0131nava girdikten sonra ka\u00e7 \u00f6\u011frencinin okudu\u011funu ve ka\u00e7\u0131n\u0131n ge\u00e7ti\u011fini \u00f6\u011frenmek i\u00e7in veriler topland\u0131. Sonu\u00e7lar a\u015fa\u011f\u0131daki beklenmedik durum tablosunda sunulmaktad\u0131r. Toplanan verilerden, daha \u00f6nce \u00e7al\u0131\u015fm\u0131\u015fsan\u0131z, s\u0131nav\u0131 ge\u00e7menin ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131 hesaplay\u0131n. <\/li>\n<\/ul>\n
    \"ko\u015fullu<\/figure>\n

    Ko\u015fullu olas\u0131l\u0131\u011f\u0131 elde etmek i\u00e7in daha \u00f6nce g\u00f6rd\u00fc\u011f\u00fcm\u00fcz form\u00fcl\u00fc uygulamal\u0131y\u0131z:<\/p>\n<\/p>\n

    \"P(\\text{aprobado}|\\text{estudiado})=\\cfrac{P(\\text{aprobado}\\cap\\text{estudiado})}{P(\\text{estudiado})}\"<\/p>\n<\/p>\n

    Bu nedenle \u00f6ncelikle bir \u00f6\u011frencinin okuyup \u00e7al\u0131\u015f\u0131p ge\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131 bulmam\u0131z gerekiyor. Bir \u00f6\u011frencinin \u00e7al\u0131\u015fma olas\u0131l\u0131\u011f\u0131n\u0131 bulmak i\u00e7in Laplace kural\u0131n\u0131 kullanmam\u0131z yeterlidir, yani \u00e7al\u0131\u015fan \u00f6\u011frenci say\u0131s\u0131n\u0131 toplam g\u00f6zlem say\u0131s\u0131na b\u00f6lmemiz gerekir:<\/p>\n<\/p>\n

    \"P(\\text{estudiado})=\\cfrac{23}{30}=0,77\"<\/p>\n<\/p>\n

    Ve bir \u00f6\u011frencinin ayn\u0131 anda \u00e7al\u0131\u015f\u0131p ge\u00e7me olas\u0131l\u0131\u011f\u0131n\u0131, \u00e7al\u0131\u015f\u0131p ge\u00e7en \u00f6\u011frenci say\u0131s\u0131n\u0131 toplama b\u00f6lerek olas\u0131l\u0131k tablosundan bulabiliriz:<\/p>\n<\/p>\n

    \"P(\\text{aprobado}\\cap<\/p>\n<\/p>\n

    Buna g\u00f6re, bir \u00f6\u011frencinin \u00e7al\u0131\u015fm\u0131\u015f olmas\u0131 durumunda s\u0131nav\u0131 ge\u00e7me olas\u0131l\u0131\u011f\u0131: <\/p>\n<\/p>\n

    \"\\begin{aligned}P(\\text{aprobado}|\\text{estudiado})&=\\cfrac{P(\\text{aprobado}\\cap\\text{estudiado})}{P(\\text{estudiado})}\\\\<\/p>\n<\/p>\n

    <\/span> Ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z olaylar\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131<\/span><\/h2>\n

    Bu b\u00f6l\u00fcmde ko\u015fullu olas\u0131l\u0131k ile ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z olaylar (veya ba\u011f\u0131ml\u0131 ve ba\u011f\u0131ms\u0131z olaylar) aras\u0131ndaki ili\u015fkinin ne oldu\u011funu g\u00f6rece\u011fiz. \u00c7\u00fcnk\u00fc her ne kadar farkl\u0131 kavramlar olsa da bu iki olay t\u00fcr\u00fc ko\u015fullu bir olas\u0131l\u0131\u011fa ba\u011fl\u0131d\u0131r.<\/p>\n

    \u0130ki olay (veya olu\u015fum), ger\u00e7ekle\u015fme olas\u0131l\u0131klar\u0131 birbirine ba\u011fl\u0131 olmad\u0131\u011f\u0131nda ba\u011f\u0131ms\u0131zd\u0131r. B\u00f6yle bir durumda iki olay\u0131n kesi\u015fimi, her bir olay\u0131n ayr\u0131 ayr\u0131 olas\u0131l\u0131\u011f\u0131n\u0131n \u00e7arp\u0131m\u0131na e\u015fde\u011ferdir. Ve bu nedenle ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fc basitle\u015ftirilmi\u015ftir:<\/p>\n<\/p>\n

    \"P(A|B)=\\cfrac{P(A\\cap<\/p>\n<\/p>\n

    K\u0131sacas\u0131, e\u011fer A ve B olaylar\u0131 ba\u011f\u0131ms\u0131zsa, belirli bir B olay\u0131 i\u00e7in A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131, A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131na tam olarak e\u015fittir.<\/strong><\/p>\n

    \u00d6te yandan, iki olay\u0131n birbirine ba\u011fl\u0131 olmas\u0131, bir olay\u0131n olas\u0131l\u0131\u011f\u0131n\u0131n di\u011fer olay\u0131n olas\u0131l\u0131\u011f\u0131na ba\u011fl\u0131 oldu\u011fu anlam\u0131na gelir. Bu nedenle, iki A ve B olay\u0131 ba\u011f\u0131ml\u0131 oldu\u011funda, belirli bir B olay\u0131 i\u00e7in A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131, A olay\u0131n\u0131n meydana gelme olas\u0131l\u0131\u011f\u0131ndan farkl\u0131d\u0131r.<\/strong> <\/p>\n<\/p>\n

    \"P(A|B)\\neq<\/p>\n<\/p>\n

    <\/span> \u00c7\u00f6z\u00fclm\u00fc\u015f ko\u015fullu olas\u0131l\u0131k egzersizleri<\/span><\/h2>\n

    1. Egzersiz<\/h3>\n

    Toplarla dolu bir torban\u0131n yar\u0131s\u0131n\u0131n turuncu, di\u011fer yar\u0131s\u0131n\u0131n ise ye\u015fil oldu\u011funu biliyoruz. Ayr\u0131ca toplar\u0131n \u00fc\u00e7te biri turuncu renktedir ve ayn\u0131 zamanda bir i\u015faretle i\u015faretlenmi\u015ftir. Turuncu bir top \u00e7ekti\u011finizde sinyali alma olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n

    \n
    \u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n

    Al\u0131\u015ft\u0131rmay\u0131 \u00e7\u00f6zmek i\u00e7in ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fcn\u00fc uygulamal\u0131y\u0131z:<\/p>\n<\/p>\n

    \"P(\\text{se\\~nal}|\\text{naranja})=\\cfrac{P(\\text{se\\~nal}\\cap\\text{naranja})}{P(\\text{naranja})}\"<\/p>\n<\/p>\n

    Sorun ifadesi bize torban\u0131n yar\u0131s\u0131n\u0131n portakal oldu\u011funu s\u00f6yl\u00fcyor. Bu nedenle turuncu bir topun al\u0131nmas\u0131n\u0131n teorik olas\u0131l\u0131\u011f\u0131 %50’dir.<\/p>\n<\/p>\n

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

    \u00d6te yandan, toplam\u0131n \u00fc\u00e7te birinin turuncu top oldu\u011funu ve sinyale sahip oldu\u011funu biliyoruz, dolay\u0131s\u0131yla sinyalli turuncu bir top elde etme olas\u0131l\u0131\u011f\u0131:<\/p>\n<\/p>\n

    \"P(\\text{se\\~nal}\\cap<\/p>\n<\/p>\n

    Son olarak, de\u011ferini bulmak i\u00e7in hesaplanan olas\u0131l\u0131klar\u0131 ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fcnde yerine koyar\u0131z:<\/p>\n<\/p>\n

    \"\\begin{aligned}P(\\text{se\\~nal}|\\text{naranja})&=\\cfrac{P(\\text{se\\~nal}\\cap\\text{naranja})}{P(\\text{naranja})}\\\\<\/p>\n<\/p>\n

    \u00d6zetle, turuncu ise sinyalli bir topun \u00e7ekilme olas\u0131l\u0131\u011f\u0131 %66’d\u0131r.<\/p>\n

    <\/div>\n

    Al\u0131\u015ft\u0131rma 2<\/h3>\n

    Bir kutuda alt\u0131 mavi kalem ve \u00fc\u00e7 siyah kalem varsa, tek bir mavi kalem \u00e7ekme olas\u0131l\u0131\u011f\u0131n\u0131 ve art arda iki mavi kalem \u00e7ekme olas\u0131l\u0131\u011f\u0131n\u0131 hesaplay\u0131n. <\/p>\n

    \n
    \u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n

    Mavi kalemi bir kez elinize alma olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in Laplace yasas\u0131n\u0131 kullanman\u0131z yeterlidir:<\/p>\n<\/p>\n

    \"P(\\text{azul})=\\cfrac{6}{6+3}=0,67\"<\/p>\n<\/p>\n

    Problem ayr\u0131ca bizden art arda iki mavi kalem alma olas\u0131l\u0131\u011f\u0131n\u0131, yani daha \u00f6nce mavi bir kalem alm\u0131\u015fsak mavi kalem alman\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131 bilmemizi istiyor.<\/p>\n

    Mavi kalem \u00e7ekersek daha az avantajl\u0131 bir durumla kar\u015f\u0131 kar\u015f\u0131ya kal\u0131r\u0131z ama toplamda bir kalem daha eksik olur. Bu nedenle ko\u015fullu olas\u0131l\u0131k: <\/p>\n<\/p>\n

    \"P(\\text{azul}|\\text{azul})=\\cfrac{5}{8}=0,63\"<\/p>\n<\/p>\n

    <\/div>\n

    Al\u0131\u015ft\u0131rma 3<\/h3>\n

    Yaz\u0131-tura at\u0131ld\u0131\u011f\u0131nda tura gelmesi ko\u015fuluyla zar\u0131n 4 rakam\u0131na gelme ko\u015fullu olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n

    \n
    \u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n

    Bu al\u0131\u015ft\u0131rmay\u0131 \u00e7\u00f6zmek i\u00e7in ko\u015fullu olas\u0131l\u0131k teorisini hesaba katmal\u0131s\u0131n\u0131z \u00e7\u00fcnk\u00fc “zar atarak 4 say\u0131s\u0131n\u0131 elde etme”<\/em> ve “para atarak tura gelme”<\/em> olaylar\u0131 ba\u011f\u0131ms\u0131zd\u0131r. Bu nedenle ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fcn\u00fc kullanmak gerekli de\u011fildir ancak a\u015fa\u011f\u0131daki e\u015fitlik sa\u011flan\u0131r:<\/p>\n<\/p>\n

    \"P(\\text{n\\'umero<\/p>\n<\/p>\n

    Dolay\u0131s\u0131yla ko\u015fullu olas\u0131l\u0131\u011f\u0131 bulmak i\u00e7in Laplace kural\u0131n\u0131 kullanman\u0131z yeterlidir: <\/p>\n<\/p>\n

    \"P(\\text{n\\'umero<\/p>\n<\/p>\n

    <\/div>\n

    Al\u0131\u015ft\u0131rma 4<\/h3>\n

    Bir \u00fclkedeki 25 \u015firketin mali y\u0131l\u0131 incelendi ve hisse senedi fiyatlar\u0131n\u0131n o y\u0131l\u0131n ekonomik sonu\u00e7lar\u0131na g\u00f6re nas\u0131l de\u011fi\u015fti\u011fi incelendi. Toplanan verileri a\u015fa\u011f\u0131daki acil durum tablosunda g\u00f6rebilirsiniz: <\/p>\n

    \"ko\u015fullu<\/figure>\n

    Bir \u015firketin ge\u00e7en y\u0131l kar elde etmesi durumunda hisse senedi fiyat\u0131n\u0131n artma olas\u0131l\u0131\u011f\u0131 nedir? <\/p>\n

    \n
    \u00c7\u00f6z\u00fcm\u00fc g\u00f6r\u00fcn<\/strong><\/div>\n<\/div>\n

    Al\u0131\u015ft\u0131rma bize, \u015firketin olumlu bir ekonomik sonu\u00e7 elde etmesi durumunda hisse senetlerinin artaca\u011f\u0131 ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131 soruyor. Dolay\u0131s\u0131yla bu olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in ko\u015fullu olas\u0131l\u0131k form\u00fcl\u00fcn\u00fc kullanmal\u0131y\u0131z:<\/p>\n<\/p>\n

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

    Bu nedenle \u00f6ncelikle bir \u015firketin k\u00e2r etme olas\u0131l\u0131\u011f\u0131n\u0131, ikinci olarak da bir \u015firketin hisse ba\u015f\u0131na fiyat\u0131n\u0131 art\u0131r\u0131rken ekonomik k\u00e2r elde etme olas\u0131l\u0131\u011f\u0131n\u0131 hesapl\u0131yoruz: <\/p>\n<\/p>\n

    \"P(\\text{beneficio})=\\cfrac{14}{25}=0,56\"<\/p>\n<\/p>\n

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

    Daha sonra bulunan de\u011ferleri form\u00fclde yerine koyar\u0131z ve ko\u015fullu olas\u0131l\u0131\u011f\u0131 hesaplar\u0131z: <\/p>\n<\/p>\n

    \"\\begin{aligned}P(\\text{precio<\/p>\n<\/p>\n

    <\/div>\n

    <\/span> Ko\u015fullu olas\u0131l\u0131\u011f\u0131n \u00f6zellikleri<\/span><\/h2>\n

    Ko\u015fullu olas\u0131l\u0131\u011f\u0131n veya ko\u015fullu olas\u0131l\u0131\u011f\u0131n \u00f6zellikleri a\u015fa\u011f\u0131daki gibidir:<\/p>\n

      \n
    • A olay\u0131n\u0131n belirli bir B olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131 art\u0131 tamamlay\u0131c\u0131 A olay\u0131n\u0131n belirli bir B olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131n\u0131n toplam\u0131 bire e\u015fittir.<\/li>\n<\/ul>\n

      \"<\/p>\n<\/p>\n

        \n
      • A olay\u0131 B olay\u0131n\u0131n bir alt k\u00fcmesi ise, B do\u011fru oldu\u011funda A her zaman meydana gelecektir. Dolay\u0131s\u0131yla bu durumlarda B olay\u0131 verildi\u011finde A olay\u0131n\u0131n ko\u015fullu olas\u0131l\u0131\u011f\u0131 1’dir.<\/li>\n<\/ul>\n

        \"B\\subseteq<\/p>\n<\/p>\n

          \n
        • \u0130ki farkl\u0131 olay g\u00f6z \u00f6n\u00fcne al\u0131nd\u0131\u011f\u0131nda, ko\u015fullu olas\u0131l\u0131\u011fa g\u00f6re a\u015fa\u011f\u0131daki e\u015fitlik her zaman ge\u00e7erlidir:<\/li>\n<\/ul>\n

          \"P\\bigl(A\\bigr)=P\\bigl(A|B\\bigr)\\cdot<\/p><\/p>\n","protected":false},"excerpt":{"rendered":"

          Burada ko\u015fullu olas\u0131l\u0131\u011f\u0131n (veya ko\u015fullu olas\u0131l\u0131\u011f\u0131n) ne oldu\u011funu \u00f6\u011freneceksiniz. Ko\u015fullu olas\u0131l\u0131\u011f\u0131n nas\u0131l hesapland\u0131\u011f\u0131n\u0131 ve bu olas\u0131l\u0131k t\u00fcr\u00fcn\u00fcn \u00f6zelliklerini bir \u00f6rnekle a\u00e7\u0131kl\u0131yoruz. Ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen ko\u015fullu olas\u0131l\u0131k al\u0131\u015ft\u0131rmalar\u0131 ile pratik yapabileceksiniz. Ko\u015fullu olas\u0131l\u0131k nedir? Ko\u015fullu olas\u0131l\u0131k , ayn\u0131 zamanda ko\u015fullu olas\u0131l\u0131k olarak da adland\u0131r\u0131l\u0131r, ba\u015fka bir B olay\u0131n\u0131n meydana gelmesi durumunda A olay\u0131n\u0131n meydana gelme […]<\/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-39","post","type-post","status-publish","format-standard","hentry","category-olasilik"],"yoast_head":"\n\u25b7 Ko\u015fullu olas\u0131l\u0131k (veya ko\u015fullu olas\u0131l\u0131k)<\/title>\n<meta name=\"description\" content=\"Ko\u015fullu olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ko\u015fullu olas\u0131l\u0131kla \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar.\" \/>\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\/kosullu-kosullu-olasilik\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Ko\u015fullu olas\u0131l\u0131k (veya ko\u015fullu olas\u0131l\u0131k)\" \/>\n<meta property=\"og:description\" content=\"Ko\u015fullu olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. Ko\u015fullu olas\u0131l\u0131kla \u00e7\u00f6z\u00fclm\u00fc\u015f al\u0131\u015ft\u0131rmalar.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-06T08:15:33+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/probabilite-conditionnelle-ou-conditionnelle.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/\",\"url\":\"https:\/\/statorials.org\/tr\/kosullu-kosullu-olasilik\/\",\"name\":\"\u25b7 Ko\u015fullu olas\u0131l\u0131k (veya ko\u015fullu olas\u0131l\u0131k)\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-06T08:15:33+00:00\",\"dateModified\":\"2023-08-06T08:15:33+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Ko\u015fullu olas\u0131l\u0131\u011f\u0131n ne oldu\u011funu ve nas\u0131l hesapland\u0131\u011f\u0131n\u0131 a\u00e7\u0131kl\u0131yoruz. 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