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5.62 A certain airplane has...

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 willfail? (b) Neither will fail? (c) One or the other will fail? Show all steps carefully.

5.63 There is a 30 percent chance that a bidding firm will get contract A and a 40 percent chance they will get contract B. There is a 5 percent chance that they will get both. Are the events independent?

5.64 A couple has two children. What is the probability that both are boys, given that the first is a boy?

5.65 On July 14, 2004, a power outage in the Northwest Airlines operations center near Minneapolis forced the airline’s computer systems to shut down, leading to cancellation of 200 flights and delays in scores of other flights. (a) Explain how the concept of statistical independence might be applicable here. (b) How would the airline decide whether, say, expenditure of $100,000 would be justified for a backup system to prevent future occurrences? (Data are from The Wall Street Journal, July 15, 2004.)

5.66 Which are likely to be independent events? For those you think are not, suggest reasons why.

a. Gender of two consecutive babies born in a hospital.

b. Car accident rates and the driver’s gender.

c. Phone call arrival rates at a university admissions office and time of day.

5.67 In child-custody cases, about 70 percent of the fathers win the case if they contest it. In the next three custody cases, what is the probability that all three win? What assumption(s) are you making?

5.68 RackSpace-managed hosting advertises 99.999 percent guaranteed network uptime. (a) How many independent network servers would be needed if each has 99 percent reliability? (b) If each has 90 percent reliability? (Data are from www.rackspace.com.)

5.69 Fifty-six percent of American adults eat at a table-service restaurant at least once a week. Suppose that four American adults are asked if they ate at table-service restaurants last week. What is the probability that all of them say yes?

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”?

5.63 There is a 30 percent chance that a bidding firm will get contract A and a 40 percent chance they will get contract B. There is a 5 percent chance that they will get both. Are the events independent?

5.64 A couple has two children. What is the probability that both are boys, given that the first is a boy?

5.65 On July 14, 2004, a power outage in the Northwest Airlines operations center near Minneapolis forced the airline’s computer systems to shut down, leading to cancellation of 200 flights and delays in scores of other flights. (a) Explain how the concept of statistical independence might be applicable here. (b) How would the airline decide whether, say, expenditure of $100,000 would be justified for a backup system to prevent future occurrences? (Data are from The Wall Street Journal, July 15, 2004.)

5.66 Which are likely to be independent events? For those you think are not, suggest reasons why.

a. Gender of two consecutive babies born in a hospital.

b. Car accident rates and the driver’s gender.

c. Phone call arrival rates at a university admissions office and time of day.

5.67 In child-custody cases, about 70 percent of the fathers win the case if they contest it. In the next three custody cases, what is the probability that all three win? What assumption(s) are you making?

5.68 RackSpace-managed hosting advertises 99.999 percent guaranteed network uptime. (a) How many independent network servers would be needed if each has 99 percent reliability? (b) If each has 90 percent reliability? (Data are from www.rackspace.com.)

5.69 Fifty-six percent of American adults eat at a table-service restaurant at least once a week. Suppose that four American adults are asked if they ate at table-service restaurants last week. What is the probability that all of them say yes?

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”?

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