These 2 questions are from Applied Statistics in Business and Economics-Chapter

Question

These 2 questions are from Applied Statistics in Business and Economics-Chapter 5. If at all possible I need the answers by Monday morning-11/1/10

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.


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”?

Explanation / Answer

1. (a) (0.02)^2 (b) (0.98)^2 (c) (0.02)(0.98)+(0.98)(0.02) 2. (a) Probability of no accidents is (3999999/4000000)^50000 = 0.9876, so the probability of a fatal accident is 0.0124. Independence might be violated because bad drivers will have a higher likelihood of a fatal accident on all trips, and good drivers will have a lower likelihood. (b) Because the chances of a fatal accident on any one trip are so low.

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