Question

An insurance company has written 50 policies for $100,000, 100 policies for $25,000, and 250 policies for $10,000 for people of age 20. If experience shows that the probability that a person will die at age 20 is 0.0012, how much can the company expect to pay out during the year the policies were written?

The company can expect to pay out $_____ over the year after the policies were written.

( type an integer or a decimal)

Answer 1

An insurance company has written 50 policies for $100,000, 100 policies for $25,000, and 250 policies for $10,000 for people of age 20. If experience shows that the probability that a person will die at age 20 is 0.0012, how much can the company expect to pay out during the year the policies were written

We first compute the amount of money the company can expect to pay out for each kind of policy. The sum of these amounts will be the total amount the company can expect to pay out.

For a single $100,000 policy,

we have the following probability distributtion
Pay Don't  Pay

Out come $100,000  $100,000

Probability 0 0012 0.9998

Suppose the random variable x can take on the value n values x₁,x₂,x₃ ,, ,,...,x_n.

Also, suppose the probabilities that these values occur are, respectively,p₁,p₂,....p_n.

Then the expected value of the random variable Is

E(x) = x₁ p₁ + x₂ p₂ + .... + x_n p_n.

E(payoff) =100,000(0.0012)+0(0.9998)

=$120

For all 50 such policies, the company can expect to pay out

50(120)=$6000

Far a single $25,000 policy,

E(Payoff)= 25,000(0.0012)+0(0.9998)

= $ 30

For all 100 such policies , the company can expected to pay out

100(30) = $3000

Similarly , for all 250 policies of $10,000, the company can expected to pay out

250(12) = $3000

Thus , the total amount the company can expect to pay out is

$6000+$3000+$3000 = $12000

The company can expect to pay out $12000 over the year after the policies were written.