# RES week4 - RES/ 5.....

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RES/341 Week 4 Answer Guide - Statistics 5.62  -A certain airplane has two independent alternators to provide electrical power. The probability that a given  alternator will fail on a 1-hour  flight  is .02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or  the other will fail? Show all steps carefully. (a) Both Fail N = 2, p = .02, a = alternator 1, b = alternator 2 Pa  Ç  Pb =  (.02)(.02) = 0.0004 The probability that both will fail is 0.0004 or 0.04% (b) Neither Will Fail 1-( Pa + Pb) + (Pa  Ç  Pb) =  (1 - 0.04) + 0.0004 = 0.9604 The probability that neither will fail is 0.9604 or 96.04% (c) One or the other will fail Pa + Pb - (Pa  Ç  Pb)=  0.02 + 0.02 – 0.0004 = 0.0396  The probability that one or the other will fail is 0.0396 or 3.96% 5.70  - * The probability is 1 in 4,000,000 that a single  auto  trip in the United States will result in a fatality. Over a  lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of a fatal accident over a lifetime?

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