Etext Paper Week 4 Res341

417 Words2 Pages
Exercises from E-Text RES/341 May 2nd 20 Question #1 (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. Answer: If the probability of failure is .02 than the probability of not failing is .98 (a) Both will fail= 0.02 * 0.02 = 0.0004 (b) Neither will fail= 0.98 * 0.98 = 0.9604 (c) One or the other will fail = 0.98 * 0.02= (0.0196) + 0.98* 0.02= (0.0196) = 0.0392 Question #2 (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? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b) Why might a driver be tempted not to use a seat belt “just on this trip”? Answer: (a) What is the probability of a fatal accident over a lifetime? 1/4,000,000 = 0.00000025 is the probability of a fatality, so therefore 0.99999975 relates to not having a fatality. N = 2, p = 0.00000025, a = fatal accident, b = no fatal accident Pa = 1 – Pb Pa = 1 – 0.00000025 Pa = 0.99999975 ^ 50000 = 0.987577799 Pa = 1 – 0.987577799 Pa = 0.012422201 or the probability of a fatal accident over a lifetime is 0.012422201 or 1.24%. One can assume independence; when we are assuming that none of our previous driving experiences had any fatal accidents does not make it any less likely that we will have an accident. Average drivers know this is not true, that the probability of a fatal accident decreases as we get more experience driving and become more mature. (b) Why might a
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