Question 185150This 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. 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”?
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? Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated?
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It's a binomial problem with n = 50,000, p = 1/4,000,000, x = 1
Using a TI-83 you get binompdf(50,000,1/400,000,000,1) = 0.01234
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Independence might be doubted because some people have a history of
having accidents and others never have an accident because they are
more careful in their driving habits.
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(b) Why might a driver be tempted not to use a seat belt “just on this trip”?
The probability on any given grip is 1/400,000 but it is more than 1/100
for a lifetime of 50,000 trips.
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Cheers,
Stan H.
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