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 th

Question 213853This question is from textbook Applied Statistics
: 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. Why might the assumption of indepenent be violated? (b) Why might a driver be tempted not to use a seat belt "just on this trip".

This question is from textbook Applied Statistics

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?
Ans: 50,000C1(1/4,000,000)^1(3,999,999/4,000,000)^49,999 = 0.01234
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Explain your reasoning carefully.
It is a binomial problem with 50,000 trials, prob. of an accident
on each trial is 4,000,000^-1, number of "successes" = 1.
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Why might the assumption of independence be violated?
The probability of having an accident when young is different
than probability of accident when older.
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(b) Why might a driver be tempted not to use a seat belt "just on this trip".
Because probability on that one trip is 1/4,000,000
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Cheers,
Stan H.
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