Question 86822: a 30 year old can purchase a one year life insurance policy for 20,000 at a cost of 25.00. The probability of a person dying at age 30 is 0.0002. What is the company's expected profit per policy?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Here's an approach to this problem.
.
If the number of policies sold is 10,000, the probability is that of this pool of policies
0.0002 is the probability of death. Multiply the 10,000 by 0.0002 and you get that 2 deaths
will occur.
.
At $25 per policy, 10,000 policies will bring in a total of $250,000 (which comes from
$25 * 10,000).
.
But the company will statistically have to pay for two policies, and since the payoff
will be $20,000 per policy for a total payoff of $40,000.
.
Therefore, the "profit" on $250,000 of income to the company will be $250,000 less the
$40,000 payoff which is $210,000.
.
Dividing this profit by the 10,000 policies that generate it will give the "per policy
profit".
.
.
Therefore, you can say that of the $25 the company collects for a policy, the policy
will typically return $21 as "profit".
.
Hope this helps you to understand the problem and a way that you can analyze it to get
an answer.
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