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?

The expected value of this policy is -$425.

Step-by-step 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:

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