Explanation Calculation: Conditional probability: The conditional probability of B given A is, P ( B | A ) = P ( A ∩ B ) P ( A ) The serial circuit system consist only the subsystem components A , B , C , D , and E and this is parallel system of two series subsystems. From Exercise 2.93, the probability that the entire system works is 0.7511. Let S denotes the system works. The probability that the component A does not work given that the system also does not work is, P ( A ' | S ' ) = P ( A ' ∩ S ' ) P ( S ' ) = P [ A ' ∩ ( C ∩ D ∩ E ) ' ]

Probability and Statistics for Engineers and Scientists

9th Edition

ISBN: 9780321629111

Author: Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye

Publisher: Prentice Hall

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Chapter 2.6, Problem 94E

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Find the probability that the component A does not work given that the system also does not work.

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Chapter 2.6, Problem 93E

Chapter 2.7, Problem 95E

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Probability and Statistics for Engineers and Scientists

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