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Statistics / Probability and Statistics for Engineers and the Scientists 9 / Chapter 2 / Problem 52E

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

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A system consists of two identical pumps, #1 and #2. If

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QUESTION:

A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, r = P(#2 fails ◊◊#1 fails) > P(#2 fails) = q. If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?

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QUESTION:

A system consists of two identical pumps, #1 and #2. If one pump fails, the system will still operate. However, because of the added strain, the remaining pump is now more likely to fail than was originally the case. That is, r = P(#2 fails ◊◊#1 fails) > P(#2 fails) = q. If at least one pump fails by the end of the pump design life in 7% of all systems and both pumps fail during that period in only 1%, what is the probability that pump #1 will fail during the pump design life?

ANSWER:

Answer: Step 1 of 1 Let A be the event that Pump #1 fails and B be the event that Pump #2 fails. We are given that: P(at least one pump fails) = 0.07 P(A or B) = 0.07 P(both pumps fail) = 0.01 P(A and B

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