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5.62 & 5.70 E-text Assignments YM

# 5.62 & 5.70 E-text Assignments YM - Why might a driver...

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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. P(both will fail) = (.02)(.02) =0.0004 P(neither will fail) = Since this is independent probability the following applies. 1 - 0.02 = 0.98 = (0.98)(0.98) = 0.9604 P(one or the other will fail) = (0.02)(0.98) + (0.98)(0.02) + 0.0004 = 0.0396 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 fatal accident over a lifetime? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated? (b)
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Unformatted text preview: Why might a driver be tempted not to use a seat belt “just on this trip”? a. P(fatal accident over a lifetime) = 1 − P(no fatal accident over a lifetime) = 1 − (3,999,999/4,000,000) 50,000 = .012422. 1. Some drivers have more experience than others at driving and learning how to avoid accidents by controlling the vehicle at all times and being aware of surroundings. 2. Drivers who recently were corrected in their driving either through police enforcement or accident (injury or non-injury) are prone to drive safer or not drive at all (such as those involved fatality involved accidents). b. The probability of an accident each time you get behind the wheel is so small that an individual might take the risk....
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