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Консультация № 194857
04.03.2019, 01:06
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Вероятности исправной работы элементов, приведённых, на схемах, равны P1=0,9;P2=0,8;P3=0,7;P4=0,6;P5=0,5. Отказ любого из элементов приводит к прерыванию сигнала в той ветви цепи, где находится элемент. Предполагается, что элементы работают независимо друг от друга. Найти вероятность прохождения сигнала через цепь.
Вероятности исправной работы элементов, приведённых, на схемах, равны P1=0,9;P2=0,8;P3=0,7;P4=0,6;P5=0,5. Отказ любого из элементов приводит к прерыванию сигнала в той ветви цепи, где находится элемент. Предполагается, что элементы работают независимо друг от друга. Найти вероятность прохождения сигнала через цепь.
Обсуждение
04.03.2019, 06:46
общий
это ответ
Здравствуйте, Evgeny20!
Сигнал пройдёт через цепь в трёх случаях:
1) элемент 1 работает, элемент 2 работает, элемент 3 работает; вероятность этого p1=0,9*0,8*0,7=0,504;
2) элемент 1 работает, элемент 2 работает, элемент 3 не работает; вероятность этого p2=0,9*0,8*(1-0,7)=0,216;
3) элемент 1 работает, элемент 2 не работает, элемент 3 работает; вероятность этого p3=0,9*(1-0,8)*0,7=0,14.
Поэтому вероятность того, что сигнал пройдёт через цепь, составляет
Сигнал пройдёт через цепь в трёх случаях:
1) элемент 1 работает, элемент 2 работает, элемент 3 работает; вероятность этого p1=0,9*0,8*0,7=0,504;
2) элемент 1 работает, элемент 2 работает, элемент 3 не работает; вероятность этого p2=0,9*0,8*(1-0,7)=0,216;
3) элемент 1 работает, элемент 2 не работает, элемент 3 работает; вероятность этого p3=0,9*(1-0,8)*0,7=0,14.
Поэтому вероятность того, что сигнал пройдёт через цепь, составляет
p=p1+p2+p3=0,504+0,216+0,14=0,86.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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