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Задать вопрос экспертам

Консультация № 176979

28.02.2010, 21:16

0.00 руб.

0 1 1

Образование

Уважаемые эксперты прошу помощи в задачке по теории вероятности!

В мастерской имеется 12 моторов. При существующем режиме работы вероятность того, что мотор в данный момент работает с полной нагрузкой, равна 0,8. Найти вероятность того, что в данный момент не менее 10 моторов работает с полной нагрузкой.

Обсуждение

давно

Орловский Дмитрий

Мастер-Эксперт
319965
1463

28.02.2010, 23:16

общий

это ответ

Здравствуйте, Dflame.

Имеем схему независимых испытаний Бернулли с вероятностью успеха p=0,8 и числом испытаний n=12.
Вероятность того, что будет k успехов определяется формулой
P_n(k)=(n!/(k!(n-k)!))p^k(1-p)^n-k
Нам нужно вычислить сумму P₁₂(10)+P₁₂(11)+P₁₂(12)
P₁₂(10)=66*0,8¹⁰*0,2²=0,2835
P₁₂(11)=12*0,8¹¹*0,2=0,2062
P₁₂(12)=0,8¹²=0,0687
Искомая величина равна 0,2835+0,2062+0,0687=0,5584

5

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