Explanation Define the events: W : { System is working } A i : { i th unit is working } ; i ∈ { 1 , 2 , 3 , 4 , 5 } The relay is marked with number from 1 to 5, which is shown below: From the Figure, it can be observed that either both relays 1 and 2 have to work, or both relays 3 and 4 have to work, or relay 5 have to work. That is, W = ( A 1 ∩ A 2 ) ∪ ( A 3 ∩ A 4 ) ∪ A 5 . It is given that, P ( units fails ) = p and P ( A i ) = 1 − p . Moreover, all events are independent. So, the events A i and A j are independent. That is, P ( A i ∩ A j ) = P ( A i ) × P ( A j ) . By using the addition rule, P ( W ) = P ( ( A 1 ∩ A 2 ) ∪ ( A 3 ∩ A 4 ) ∪ A 5 ) = { P ( A 1 ∩ A 2 ) + P ( A 3 ∩ A 4 ) + P ( A 5 ) − P ( ( A 1 ∩ A 2 ) ∩ ( A 3 ∩ A 4 ) ) − P ( ( A 1 ∩ A 2 ) ∩ A 5 ) − P ( ( A 3 ∩ A 4 ) ∩ A 5 ) + P ( ( A 1 ∩ A 2 ) ∩ ( A 3 ∩ A 4 ) ∩ A 5 ) } = { P ( A 1 ) P ( A 2 ) + P ( A 3 ) P ( A 4 ) + P ( A 5 ) − P ( A 1 ) P ( A 2 ) P ( A 3 ) P ( A 4 ) − P ( A 1 ) P ( A 2

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ISBN: 9780100244702

Author: RICE

Publisher: YUZU

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Question

Chapter 1.8, Problem 74P

To determine

Find the probability that the given system works if each unit fails independently with probability p.

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Chapter 1 Solutions

EBK MATHEMATICAL STATISTICS AND DATA AN

Ch. 1.8 - Prob. 1P Ch. 1.8 - Prob. 2P Ch. 1.8 - Prob. 3P Ch. 1.8 - Prob. 4P Ch. 1.8 - Prob. 5P Ch. 1.8 - Prob. 6P Ch. 1.8 - Prob. 7P Ch. 1.8 - Prob. 8P Ch. 1.8 - Prob. 9P Ch. 1.8 - Prob. 10P

Ch. 1.8 - Prob. 11P Ch. 1.8 - Prob. 12P Ch. 1.8 - Prob. 13P Ch. 1.8 - Prob. 14P Ch. 1.8 - Prob. 15P Ch. 1.8 - Prob. 16P Ch. 1.8 - Prob. 17P Ch. 1.8 - Prob. 18P Ch. 1.8 - Prob. 19P Ch. 1.8 - Prob. 20P Ch. 1.8 - Prob. 21P Ch. 1.8 - Prob. 22P Ch. 1.8 - Prob. 23P Ch. 1.8 - Prob. 24P Ch. 1.8 - Prob. 25P Ch. 1.8 - Prob. 26P Ch. 1.8 - Prob. 27P Ch. 1.8 - Prob. 28P Ch. 1.8 - Prob. 29P Ch. 1.8 - Prob. 30P Ch. 1.8 - Prob. 31P Ch. 1.8 - Prob. 32P Ch. 1.8 - Prob. 33P Ch. 1.8 - Prob. 34P Ch. 1.8 - Prob. 35P Ch. 1.8 - Prob. 36P Ch. 1.8 - Prob. 37P Ch. 1.8 - Prob. 38P Ch. 1.8 - Prob. 39P Ch. 1.8 - Prob. 40P Ch. 1.8 - Prob. 41P Ch. 1.8 - Prob. 42P Ch. 1.8 - Prob. 43P Ch. 1.8 - Prob. 44P Ch. 1.8 - Prob. 45P Ch. 1.8 - Prob. 46P Ch. 1.8 - Prob. 47P Ch. 1.8 - Prob. 48P Ch. 1.8 - Prob. 49P Ch. 1.8 - Prob. 50P Ch. 1.8 - Prob. 51P Ch. 1.8 - Prob. 52P Ch. 1.8 - Prob. 53P Ch. 1.8 - Prob. 54P Ch. 1.8 - Prob. 55P Ch. 1.8 - Prob. 56P Ch. 1.8 - Prob. 57P Ch. 1.8 - Prob. 59P Ch. 1.8 - Prob. 60P Ch. 1.8 - Prob. 61P Ch. 1.8 - Prob. 62P Ch. 1.8 - Prob. 63P Ch. 1.8 - Prob. 64P Ch. 1.8 - Prob. 65P Ch. 1.8 - Prob. 66P Ch. 1.8 - Prob. 67P Ch. 1.8 - Prob. 68P Ch. 1.8 - Prob. 69P Ch. 1.8 - Prob. 70P Ch. 1.8 - Prob. 71P Ch. 1.8 - Prob. 72P Ch. 1.8 - Prob. 73P Ch. 1.8 - Prob. 74P Ch. 1.8 - Prob. 75P Ch. 1.8 - Prob. 77P Ch. 1.8 - Prob. 78P Ch. 1.8 - Prob. 79P Ch. 1.8 - Prob. 80P

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Find the probability that the given system works if each unit fails independently with probability p .

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Find the probability that the given system works if each unit fails independently with probability p.

Chapter 1 Solutions