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Консультация № 188593
04.01.2016, 16:46
0.00 руб.
04.01.2016, 17:38
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
На трех станках различной марки изготавливают однотипные детали. Производительность 1-ого станка составляет 30 деталей за смену, 2-ого и 3-ого станков - по 35 деталей. Установлено, что дефекты имеют соответственно 3% деталей, изготовленных на первом станке, 3% и 2 % деталей, изготовленных на втором и третьем станках.
а) В конце смены для контроля наугад взята одна деталь. Какова вероятность того, что взятая деталь без дефекта?
б) Наугад для контроля взяли деталь. Деталь оказалась без дефекта. Найти вероятность того, что взятая деталь изготовлена на первом станке?
СПАСИБО!
На трех станках различной марки изготавливают однотипные детали. Производительность 1-ого станка составляет 30 деталей за смену, 2-ого и 3-ого станков - по 35 деталей. Установлено, что дефекты имеют соответственно 3% деталей, изготовленных на первом станке, 3% и 2 % деталей, изготовленных на втором и третьем станках.
а) В конце смены для контроля наугад взята одна деталь. Какова вероятность того, что взятая деталь без дефекта?
б) Наугад для контроля взяли деталь. Деталь оказалась без дефекта. Найти вероятность того, что взятая деталь изготовлена на первом станке?
СПАСИБО!
Обсуждение
04.01.2016, 17:22
общий
это ответ
Здравствуйте, Посетитель - 399202!
Обозначим гипотезы A1, A2, A3 - деталь изготовлена на соответствующем станке.
B - деталь без дефектов.
Поскольку всего за смену изготовлено 100 деталей, вероятности вытащить деталь с каждого из станков
P(A1)=0,3
P(A2)=0,35
P(A3)=0,35
Вероятность, что деталь, изготовленная на конкретном станке, не имеет дефекта
P(B|A1)=0,97
P(B|A2)=0,97
P(B|A3)=0,98
Поскольку события A1, A2, A3 несовместимы, вероятность, что случайная деталь не имеет дефекта
P(B)=P(A1)[$183$]P(B|A1)+P(A2)[$183$]P(B|A2)+P(A3)[$183$]P(B|A3)=0,9735=97,35%
Поскольку из всей продукции, не имеющих дефекта деталей, изготовленных на первом станке
P(A1[$8745$]B)=P(A1)[$183$]P(B|A1)=0,291
то вероятность найти среди не имеющих дефекта деталей деталь, изготовленную на первом станке
P(A1|B)=P(A1[$8745$]B)/P(B)=P(A1)[$183$]P(B|A1)/P(B)=0,2989...=29,89%
Обозначим гипотезы A1, A2, A3 - деталь изготовлена на соответствующем станке.
B - деталь без дефектов.
Поскольку всего за смену изготовлено 100 деталей, вероятности вытащить деталь с каждого из станков
P(A1)=0,3
P(A2)=0,35
P(A3)=0,35
Вероятность, что деталь, изготовленная на конкретном станке, не имеет дефекта
P(B|A1)=0,97
P(B|A2)=0,97
P(B|A3)=0,98
Поскольку события A1, A2, A3 несовместимы, вероятность, что случайная деталь не имеет дефекта
P(B)=P(A1)[$183$]P(B|A1)+P(A2)[$183$]P(B|A2)+P(A3)[$183$]P(B|A3)=0,9735=97,35%
Поскольку из всей продукции, не имеющих дефекта деталей, изготовленных на первом станке
P(A1[$8745$]B)=P(A1)[$183$]P(B|A1)=0,291
то вероятность найти среди не имеющих дефекта деталей деталь, изготовленную на первом станке
P(A1|B)=P(A1[$8745$]B)/P(B)=P(A1)[$183$]P(B|A1)/P(B)=0,2989...=29,89%
5
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