SOLUTION: 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

Question 230751: 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 robability 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?
The probability of no fatal accident in 50,000 trips is
(3,999,999/4,000,000)^(50,000) = 0.987578.....
So the probability of having a fatal accident is 1-0.987578... = 0.0124...
The probability changes from youth to middle age to old age.
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(b) Why might a driver be tempted not to use a seat belt �just on this trip�?
Because the probability is so small on each individual trip.
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Cheers,
Stan H.
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