An insurance company is going to charge 720 for a 1year 1500

An insurance company is going to charge $720 for a 1-year $150000 policy for women who don\'t smoke and are 44 years old. The probability that this group of women will die in the next year is 0.0046.

What is the probability of this group of women living? (write as a decimal, not a %, rounded to 4 decimal places)

What is the Expected Value of this policy for the insurance company? $ per policy How much money would 2200 policies like this generate for the insurance compan

Solution

P[Women of this group live] = 1- 0.0046 = 0.9954

Let A denote the event that a woman of this group dies in the next year.

Given P(A)=0.0046

Let X be the value of this policy for the insurance company.

Then X = -(150000-720) = - 149280 if A occurs

           = 720 if A does not occur

Then P[X= - 149280] = P(A) = 0.0046

and P[X=720] = P(A^c) = 0.9954

Hence the expected value is

E(X) = -149280*0.0046 + 720*0.9954 = 30

Henc the expected value of this policy for the insurance company is $30.

In 2200 policies the comapny will expect to make $(30*2200) = $66000.