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Задать вопрос экспертам

Консультация № 178561

22.05.2010, 16:31

0.00 руб.

0 2 2

Образование

Доброе время суток уважаемые эксперты.
Задача по теории вероятностей.
Электронная схема состоит из 3-х блоков, работающих независимо друг от друга. Вероятность того, что каждый из них работает исправно соответственно равны р₁=0.8, р₂=0.4, р₃=0.7. Схема годна к эксплуатации при наличии двух исправных блоков из 3-х. Определить вероятность того, что электронная схема будет работать.

Обсуждение

Неизвестный

22.05.2010, 22:39

общий

это ответ

Здравствуйте, LfiN.
Электронная схема работает, если:
1) исправны все три блока, вероятность этого p₁*p₂*p₃ = 0.8*0.4*0.7 = 0.22
2) исправны ровно два блока и один неисправен, вероятность этого
p₁*p₂*(1 - p₃) + p₁*(1 - p₂)*p₃ + (1 - p₁)*p₂*p₃ = 0.8*0.4*0.3 + 0.8*0.6*0.7 + 0.2*0.4*0.7 = 0.49
Общая вероятность, того что схема работает есть 0.22 + 0.49 = 0.71
Ответ: 0.71

5

Благодарю

Неизвестный

23.05.2010, 20:19

общий

это ответ

Здравствуйте, LfiN.

Обозначим событие, состоящее в исправности i-блока как Pi
Обозначим событие, состоящее в неисправности i-блока как Qi.

Тогда искомое событие состоит в:

A = P1*P2*Q3 + Q1*P2*P3 + P1*Q2*P3 + P1*P2*P3

P(A) = 0,8*0,4*0,3 + 0,2*0,4*0,7 +0,8*0,6*0,7 + 0,8*0,4*0,7 = 0,712

5

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