Question 230751
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.
----------------------------------------------------------------- 
(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.
===============================
Cheers,
Stan H.