Hodisa va uning ehtimolligi

To`la ehtimollik va Bayes formulalari bo`yicha yechiladigan masalalar

1. 
   Paxta zavodiga birinchi fermer xo`jaligi 50%, ikkinchi fermer xo`jaligi 20%, uchinchi fermer xo`jaligi 30% mahsulot beradi. Undan birinchi fermer xo`jaligi mahsulotining 70%, ikkinchi fermer xo`jaligining 85%, uchinchi fermer xo`jaligining 95% birinchi nav bo`lsa, tavakkaliga tekshirish uchun olingan tolaning birinchi nav bo`lish ehtimolini toping. Tekshirishda birinchi nav deb topilgan mahsulotning birinchi fermerga tegishli bo`lish ehtimolini toping.
   

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2. 
   Ikkita yashikda detallar bor. Birinchi yashikdagi detalning standart bo`lish ehtimoli 0,8 ga, ikkinchi yashikdagi detalning standart bo`lishi esa 0,9 ga teng. Tavakkaliga olingan detalning standart bo`lish ehtimolini toping. Standart deb topilgan detalning ikkinchi yashikdan olingan bo`lish ehtimolini toping.
   

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3. 
   Sportchilar gruppasida 20 chang`ichi, 6 velosipedchi va 4 yuguruvchi bor. Saralash normasini bajarish ehtimoli chang`ichi uchun 0,9, velosipedchi uchun 0,8, yuguruvchi uchun 0,75. Tavakkaliga ajratilgan sportchining normani bajara olish ehtimolini toping.
   

Javob:

4. 
   Birinchi yashikda 20 ta detal bo`lib, ulardan 15 tasi standart; ikkinchi yashikda 30 ta detal bo`lib, ulardan 24 tasi standart; uchinchi yashikda 10 ta detal bo`lib, ul;ardan 6 tasi standart. Tavakkaliga tanlangan yashikdan tavakkaliga olingan detalning standart bo`lish ehtimolini toping. Standart deb topilgan detalning uchinchi yashikdan olingan detal bo`lish ehtimolini toping.
   

Javob:

5. 
   Zavod sexida tayyorlanadigadetallarning standartliligini tekshirish uchun ikki nazoratchidan biriga tushadi. Detalning birinchi nazoratchiga tushish ehtimoli 0,6 ga, ikkinchi nazoratchiga tushish ehtimoli 0,4 ga teng. Yaroqli detalning standart deb tan olinish ehtimoli birinchi nazoratchi uchun 0,94 ga, ikkinchi nazoratchi uchun 0,98 ga teng. Tekshirish vaqtida yaroqli detal standart deb qabul qilindi. Shu detalni birinchi nazoratchi tekshirganlik ehtimolini toping.
   

Javob:

6. 
   A, B, C va D hodisalar to`la gruppa tashkil etadi. Hodisalarning ehtimollari bunday: P(A)=0,4; P(B)=0,2; P(C)=0,3. D hodisaning ehtimoli qanchaga teng?
   

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7. 
   Birinchi qutida 20 ta Ld lampa bo`lib, ulardan 18 tasi standart; ikkinchi qutida esa 10 ta Ld lampa bo`lib, ulardan 9 tasi standart. Ikkinchi qutidan tavakkaliga bitta lampa olinib, birinchi qutiga solingan. Birinchi qutidan tavakkaliga olingan lampaning standart bo`lish ehtimolini toping.
   

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