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

Algebra ->  Probability-and-statistics -> 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      Log On


   

Question 126741: 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 MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If we say that the probability of no+fatal accidents in a lifetime is P and the probability of having one (or more) fatal accidents in a lifetime isp, then we have:
p=1-P=1-%283999999%2F4000000%29%5E50000+=0.0124 (or about 1.2%)
-or 1+-+p+=P that is the probability that you survive each and every journey
a)
Why the independence assumption might be violated?
hmmm, that is more question of “psychology” then statistics
-overconfidence, less care when driving, doing other things in same time, and
so on, could cause p
(b) Why might a driver be tempted not to use a seat belt “just on this trip”?
it might be he/she was thinking about P....
(:-))))
many drivers think "it didn't happened to me never before, so it shouldn't happen now too"