Question

When all factors are taken into account, an insurance company estimates that the probability of my father making a claim for damages to his pontoon boat for $5000 is 0.1, and that the probability of the pontoon boat being totally destroyed is .005. Should that tragedy happen, the company will have to pay $15,000. The company charges my father $1000 for the insurance policy. What is the expected value of this policy to my father?

Answer 1

The expected value of this policy is -$425.

Explanation:

The probability distribution for the claim for damages is as follows:

Amount to be received Probability

$5,000 - $1,000 = $4,000 0.10

$15,000 - $1,000 = $14,000 0.005

-$1,000 0.895

TOTAL 1.000

Compute the expected value of this policy as follows:

`E(X)=\sum x\cdot P(X=x) \\\\`

`=(4000* 0.10)+(14000* 0.005)-(1000* 0.895)\\\\=400+70-895\\\\=-425`

Thus, the expected value of this policy is -$425.