There is a 0.9968 probability that a randomly selected 50-year-old female will live through the year. A 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 the year?

b. What are the probabilities associated with the two events, surviving and not surviving?

c. If a 50-year-old female purchases the policy, what is her expected value?

d. Can the insurance company expect to make a profit from many such policies? Why?