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Консультация № 186225
28.05.2012, 17:11
79.20 руб.
28.05.2012, 17:15
0
3
2
Здравствуйте! Прошу помощи в следующих вопросах:
1. Среди поступающих на сборку деталей с первого станка 0,2% бракованных, со второго - 0,3%, с третьего - 0,25%, с четвертого - 0,4%. Производительности их относятся, как 1:3:2:4 соответственно. Взятая наудачу деталь оказалась стандартной. Найти вероятность того, что она изготовлена на четвертом станке.
2. На машинном дворе стоят 50 тракторов. Известно, что вероятность отказа двигателя трактора равна 0,2. Определить вероятность того, что окажутся неисправными двигатели у 6 тракторов.
1. Среди поступающих на сборку деталей с первого станка 0,2% бракованных, со второго - 0,3%, с третьего - 0,25%, с четвертого - 0,4%. Производительности их относятся, как 1:3:2:4 соответственно. Взятая наудачу деталь оказалась стандартной. Найти вероятность того, что она изготовлена на четвертом станке.
2. На машинном дворе стоят 50 тракторов. Известно, что вероятность отказа двигателя трактора равна 0,2. Определить вероятность того, что окажутся неисправными двигатели у 6 тракторов.
Обсуждение
28.05.2012, 17:16
общий
Уважаемые эксперты, обратите, пожалуйста, внимание на вопрос
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
28.05.2012, 17:27
общий
это ответ
Здравствуйте, Дмитрий!
2.
Имеем схему Бернулли с 50 испытаниями. Произошло ровно 6 "успехов", причём вероятность "успеха" - 0.2. Т.о.
.
2.
Имеем схему Бернулли с 50 испытаниями. Произошло ровно 6 "успехов", причём вероятность "успеха" - 0.2. Т.о.
.
28.05.2012, 17:28
общий
это ответ
Здравствуйте, Дмитрий!
1
А - деталь стандартная
Нi - деталь изготовлена на і-ом станке
x+3x+2x+4x=100 -> x= 10 -> P(H1)=0,1, P(H2)=0,3, P(H3)=0,2, P(H4)=0,4
По формуле полной вероятности Р(А)=P(H1)P(A|H1)+P(H2)P(A|H2)+P(H3)P(A|H3)+P(H4)P(A|H4)=0,1*(1-0,002)+0,3*(1-0,003)+0,2*(1-0,0025)+0,4*(1-0,004)=0,9968
Используя формулу Байеса: P(H4|A)=P(H4)*P(A|H4)/P(A)=0,4*(1-0,004)/0,9968~0,4
1
А - деталь стандартная
Нi - деталь изготовлена на і-ом станке
x+3x+2x+4x=100 -> x= 10 -> P(H1)=0,1, P(H2)=0,3, P(H3)=0,2, P(H4)=0,4
По формуле полной вероятности Р(А)=P(H1)P(A|H1)+P(H2)P(A|H2)+P(H3)P(A|H3)+P(H4)P(A|H4)=0,1*(1-0,002)+0,3*(1-0,003)+0,2*(1-0,0025)+0,4*(1-0,004)=0,9968
Используя формулу Байеса: P(H4|A)=P(H4)*P(A|H4)/P(A)=0,4*(1-0,004)/0,9968~0,4
5
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