Review Problem 1.15 A system of electrical components is deviced as follows: re

Question

Review Problem 1.15 A system of electrical components is deviced as follows: re are two parallel subsysten . Subsystem A consists of Component 1 and Subsystem C, in series. Component 1 and Subsystem series. Subsystem C consists of Component 2 and Component 3 in parallel. . Subsystem B consists of Component 4 and Component 5 in series. Please refer to the accompanying solution video if you're having difficulty drawing this system of components. The components work independently of one another so that P(component works) Find the probability that the system works. 0.95

Explanation / Answer

P(A works) = P(1 works)*P(2 works)*P(3 does not work) + P(1 works)*P(3 works)*P(2 does not work) + P(1 works)*P(2 works)*P(3 works) = 0.95*0.95*0.05 + 0.95*0.95*0.05 + 0.95*0.95*0.95 = 0.947625

P(B works) = P(4 works)*P(5 works) = 0.95*0.95 = 0.9025

P(system works) = P(A works)*P(B works) + P(A works)*P(B does not work) +  P(B works)*P(A does not work) = 0.947625*0.9025 + 0.947625*(1-0.9025) + (1-0.947625)*0.9025 = 0.9948934375

Rounding this value we get:

P(system works) = 0.995

Hope this helps !

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