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# Consider the system of components connected as in the

ISBN: 9780321629111 32

## Solution for problem 80E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 80E

Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one another and P(component works) = .9, calculate ?P(? system works).

Step-by-Step Solution:

Answer : Step 1 : Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works if both 3 and 4 work. one another and P(component works) = .9, calculate P(system works). Let Ai = {element works } where i = 1,2,3,4 The probability of any component working is independent of any other one working. So,P(A ) = P(A ) = P(A ) = P(A ) = 0.9 1 2 3 4 The system will work if 1 or 2 works, or 1 and 2 work, or 3 and 4 work, or 1 or 2 and 3 and 4 work, or if all four elements work. Thatâ€™s seven ways in total. That number is irrelevant, but you may want to see if you can see them all. There are two main equations used in this problem. First, in calculating the union of two events, or in this case two...

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