Question 126740: 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? 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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Since prob of an accident is independent
P(accident over a lifetime)= 50,000*(1/4,000,000) = 50/4000 = 5/400 = 0.0125
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Independence might not apply because the probability of an accident
may change with age.
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Probability of an accident on "this trip" is 1/4 million = 0.00000025
which seems very low.
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Cheers,
Stan H.
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