Question 135273: 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 by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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?
P = np = 1/4000000 * 50000 = 0.0125
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Explain your reasoning carefully. Hint: Assume independent
events.
Each trip is a binomial experiment; you either have an accident or you don't.
The expected value = np = # of trials * probability of "success" on each trial.
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Why might the assumption of independence be violated?
Hopefully a person becomes a more careful driver as he gains more experience.
so the probability of having an accicentchanges with experience.
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(b) Why might a driver be tempted not to use a seat belt “just on this trip”?
He might look at the enormously small probability of an accident on this trip
and conclude the low probability somehow protects him.
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Cheers,
Stan H.
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