Exam 2 STAT 3010-090 Note: This is a CLOSED BOOK test. Total (100 pt.) (24 pt.)

Question

Exam 2 STAT 3010-090 Note: This is a CLOSED BOOK test. Total (100 pt.) (24 pt.) (16 pt.) (18 pt.) (18 pt.) (24 pt.) 1. Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works when either 1 or 2 works; since 3 and 4 are connected in series, that subsystem works when both 3 and 4 work. Assume all components work independently of one another, and all components are the same and that P(component works)- 0.9. 3 a) Calculate the probability that either 1 or 2 works, i.e., P(I n2). (8 pt) b) Calculate the probability that both 3 and 4 works, i.e., P (3 U 4). (8 pt) c) Calculate P(system works). (8 pt)

Explanation / Answer

Given that all the components are work independently

a) P(either 1 or 2 works) = 0.9 + 0.9 - P(both work) = 1.8 - (0.9)^2 = 1.8 - 0.81 = 0.99

b) P(both 3 and 4 works) = 0.9*0.9 = 0.81.

c) P(system works) = P(both 3 and 4 works or either 1 or 2 works) = 0.99 + 0.81 - P(1,3,4 works or 2,3,4) = 1.8 - (2*0.9^3) = 0.342

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