Question

There is a 0.9991 probability that a randomly selected 31​-year-old male lives through the year. A life insurance company charges ​$166 for insuring that the male will live through the year. If the male does not survive the​ year, the policy pays out ​$90 comma 000 as a death benefit. Complete parts​ (a) through​ (c) below.
a. From the perspective of the 31-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
b. If the 31-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

Answer:

a) Monetary values corresponding to the two events are:

-In case of surviving the year = -166$

-In case of a death in the year = 89834$

b) Expected value of the purchasing the insurance is -85 $

c) Yes, insurance company can make a profit with this policy.

Step-by-step explanation:

a) The man need to pay 166$ first to enroll the insurance policy. If he survives within a year, he will lose 166$. Otherwise, if he dies within a year he will profit 89834$.

b) Expected value of the purchasing the insurance as following:

-In case of surviving the year:

Value: -166$

Probability: 0,9991

-In case of death in a year

Value: 89834$

Probability: 0,0009

Expected value is E(x) = -166×0,9991 + 89834×0,0009 = -85 $

c) Lets consider that 10000 different 31 year old man enrolled to this insurance policy. According to probability of death, 9 out of 10000 man expected to be dead within the year. Therefore, company need to pay 9*90000 = 810000$ to their costumers. But, company will collect 10000*166=1660000$ from their costumers in the beginning of the year

So, it is expected that company is going to profit 1660000-810000=850000$ per year.