Exercises 5.62 and 5.70

Exercises 5.62 and 5.70 - Each trip taken in the United...

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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 (a) both will fail .02 x .02 = .0004 (b) neither will fail .98 x .98 = .9604 (c) one or the other will fail .02 x .98 + .98 x .02 = .0392 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) The probability of a fatal accident in ones lifetime.
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Unformatted text preview: Each trip taken in the United States adds a 1/ 4,000,000 th chance for a fatal accident to occur. Therefore, the probability of a fatal accident in a lifetime is; 50,000 x 1/ 4,000,000 = 5/400 = .0125 There are many variables that contribute to this; therefore, it is unlikely that this would be independent. For example, experienced drivers are less likely to have and accident. Someone with little driving experience may be more accident prone, and may take fewer trips. People who are in fatal accidents take fewer trips because their life has ended. Among other factors such as the area driven in and amount of other drivers on the road will also affect the data. (b) The likelihood of a fatal accident is minuscule and he or she may be confident his or her Experience will keep this from happening....
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