There is a 0.9968 probability that a randomly selected 50-year-old female lives through the year (based on data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges $226 for insuring that the female will live through the year. If she does not survive the year, the policy pays out $50,000 as a death benefit.
a. From the perspective of the 50-year-old female, what are the values corresponding to the two events of surviving the year and not surviving.
b. If a 50-year-old female purchases the policy, what is her expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?