The probability is 1 in 4,000,000 that a single auto trip in the ?

Question

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 1

Let's instead figure the probability of surviving over a lifetime.

One one trip, P(survival) = 1 - 1/4,000,000 = 3,999,999/4,000,000

The probability of survival on 50,000 trips would be:

= (3,999,999/4,000,000)^50,000

= 0.987577799

= 98.76% (approx.)

Thus the probability of fatality over a lifetime is 1 - 0.9876

= 1.24% (approx.)

I'll leave part B to you... personally I *always* wear my seatbelt regardless.