Professor Stern has three cars. The probability that on a given day car 1 is ope

Question

Professor Stern has three cars. The probability that on a given day car 1 is operative is 0.96, that car 2 is operative is 0.97, and that car 3 is operative is 0.85. If Professor Stern's cars operate independently, find the probability that on next Thanksgiving day (a) all three of his cars are operative; (b) at least one of his cars is operative; (c) at most two of his cars are operative; (d) none of his cars is operative. Do Problem 5 on page 129 (Chapter 3 Review Problems) of your text, but change the reliabilities of the cars to 0.96, 0.94, and 0.92. Then answer the same questions as in the text.

Explanation / Answer

a. 0.96*0.94*0.92

b.1- probability that none of the cars are operative = 1-(0.04*0.06*0.08) = 0.9998

c.1- probability that exactly one car is operative = 1-(0.96*0.06*0.08+0.04*0.94*0.08+0.04*0.06*0.92) = 0.9901

d. 0.04*0.06*0.08 = 0.000192

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