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Консультация № 138596
29.05.2008, 22:50
0.00 руб.
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Друзья помогите пожалуйтса решить задачу по теории вероятности
Завод отправил на базу 500 деталей. Вероятность повреждения изделия в пути равна 0,002. Найти вероятность того, что в пути повреждено изделий: а) ровно три, б) более трёх, в) хотя бы одно.
Буду очень рад любой помощи в решении. Спасибо
Завод отправил на базу 500 деталей. Вероятность повреждения изделия в пути равна 0,002. Найти вероятность того, что в пути повреждено изделий: а) ровно три, б) более трёх, в) хотя бы одно.
Буду очень рад любой помощи в решении. Спасибо
Обсуждение
Неизвестный
30.05.2008, 11:06
общий
это ответ
Здравствуйте, Трефилов Юрий Сергеевич!
а) вероятность того, что в пути повреждено ровно три изделия вычисляется по формуле Бернулли:
P(А3) = C(n,k)* p**k *(1-p)**(n-k) = С(500,3) * 0,002**3 * 0,998**497 = 0,06125163
б) Событие заключающееся в том, что в пути повреждено ровно более трех изделий состоит из обратного события:
А>3 = 1-(А0+A12+A2+A3)
A0- Поврежедено 0 изделий
A1- Поврежедено 1 изделие
A2- Поврежедено 2 изделия
A3- Поврежедено 3 изделия
P(А0) = С(500,0) * 0,002**0 * 0,998**500 = 0,367511255
P(А1) = С(500,1) * 0,002**1 * 0,998**499 = 0,36824775
P(А2) = С(500,2) * 0,002**2 * 0,998**498 = 0,184123875
P(А3) = С(500,3) * 0,002**3 * 0,998**497 = 0, 06125163
P(А>3) = 0,08011712
б) Событие заключающееся в том, что в пути повреждено хотя бы одно изделие состоит из обратного события:
А>1 = 1-A0
A0- Поврежедено 0 изделий
P(А0) = С(500,0) * 0,002**0 * 0,998**500 = 0,367511255
P(А>1) = 0,632488745
а) вероятность того, что в пути повреждено ровно три изделия вычисляется по формуле Бернулли:
P(А3) = C(n,k)* p**k *(1-p)**(n-k) = С(500,3) * 0,002**3 * 0,998**497 = 0,06125163
б) Событие заключающееся в том, что в пути повреждено ровно более трех изделий состоит из обратного события:
А>3 = 1-(А0+A12+A2+A3)
A0- Поврежедено 0 изделий
A1- Поврежедено 1 изделие
A2- Поврежедено 2 изделия
A3- Поврежедено 3 изделия
P(А0) = С(500,0) * 0,002**0 * 0,998**500 = 0,367511255
P(А1) = С(500,1) * 0,002**1 * 0,998**499 = 0,36824775
P(А2) = С(500,2) * 0,002**2 * 0,998**498 = 0,184123875
P(А3) = С(500,3) * 0,002**3 * 0,998**497 = 0, 06125163
P(А>3) = 0,08011712
б) Событие заключающееся в том, что в пути повреждено хотя бы одно изделие состоит из обратного события:
А>1 = 1-A0
A0- Поврежедено 0 изделий
P(А0) = С(500,0) * 0,002**0 * 0,998**500 = 0,367511255
P(А>1) = 0,632488745
Форма ответа
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