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Консультация № 174361
19.11.2009, 11:46
0.00 руб.
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1
1
Вся продукция проверяется двумя контроллерами. Вероятность того, что изделие попадет на проверку к первому контроллеру, равна 0,55, а ко второму - 0,45. Вероятность пропустить нестандартное изделие для первого контроллера равна 0,01, для второго - 0,02. Взятое наудачу изделие с маркой "стандарт" оказалось бракованным. Какова вероятность, что изделие проверялось вторым контроллером?
Заранее спасибо.
Заранее спасибо.
Обсуждение
Неизвестный
19.11.2009, 15:24
общий
это ответ
Здравствуйте, Александров Анатолий Олегович.
Задача на применение формулы Байеса
Пусть событие А – что изделие оказалось браком
Гипотезы
Нi – изделие ушло к i-му контроллеру;
Вероятности гипотез: р(Н1)=0,55, р(Н2)=0,45
Условные вероятности
р(А/Н1)=0,01, р(А/Н2)=0,02
По формуле полной вероятности
P(A) = P(Н1) P(А/Н1) + P(Н2) P(А/Н2) = 0,55*0,01+0,45*0,02 = 0.0145
То есть, вероятность пропустить брак = 0.0145
По формуле Байеса вероятность, что изделие проверялось вторым контроллером:
P(/Н2/A) = P(Н2) P(А/Н2)/P(A) = 0,45*0,02 /0.0145 = 0.620689655
Задача на применение формулы Байеса
Пусть событие А – что изделие оказалось браком
Гипотезы
Нi – изделие ушло к i-му контроллеру;
Вероятности гипотез: р(Н1)=0,55, р(Н2)=0,45
Условные вероятности
р(А/Н1)=0,01, р(А/Н2)=0,02
По формуле полной вероятности
P(A) = P(Н1) P(А/Н1) + P(Н2) P(А/Н2) = 0,55*0,01+0,45*0,02 = 0.0145
То есть, вероятность пропустить брак = 0.0145
По формуле Байеса вероятность, что изделие проверялось вторым контроллером:
P(/Н2/A) = P(Н2) P(А/Н2)/P(A) = 0,45*0,02 /0.0145 = 0.620689655
Форма ответа
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