Question

There is a 0.9989 probability that a randomly selected 29-year-old male lives through the year. A life insurance company charges $197 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit.

Required:
a. From the perspective of the 29-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 29-year-old male purchases the policy, what is his expected value?
c. Can the insurance company expect to make a profit from many such policies? Why?

Answer 1

A) - Value that corresponds to surviving the year would be: $-197

- Value Corresponding to not surviving = $98803

B) $-88.1

C) Yes, because the insurance company expects to make an average profit of $88.1 on every 29 year-old male that it insures for 1 year.

Explanation:

A) We are told that the life insurance company charges $197 for insuring that the male will live through the year.

Thus, the value that corresponds to surviving the year would be: $-197 since amount that's paid out is $-197

We are told that the policy pays out $100,000 as a death benefit.

Therefore, the value that corresponds to not surviving the year is:

$100000 - 197 = $98803

B) From complement rule in probability;

P(not surviving) = 1 - P(surviving) = 1 - 0.9989 = 0.0011

Expected value would be;

μ = Σx•P(x) = (98803 × 0.0011) + (-197 × 0.9989) = $-88.1

C) Yes, because the insurance company expects to make an average profit of $88.1 on every 29 year-old male that it insures for 1 year.