Accident records collected by an automobile insurance company give the following information. The probability that an insured driver has an automobile accident is 0.15. If an accident occurred, the damage to the vehicle amounts to 20% of its market value with a probability of 0.80, to 60% of its market value with a probability of 0.12, and to a total loss with a probability of 0.08. What premium should the company charge on a $4000 car so that the expected gain by the company is zero?

Probability of 20% loss (= $800) = .15 times .80 = .12

Probability of 60% loss (=$2400) = .15 times .12 = .018

Probability of 60% loss (= $4000) = .15 times .08 = .012

Expected Loss = 800 times .12 + 2400 times .018 + 4000 times .012

= 96 + 43.20 + 48

= $187.20

Premium = $187.20

I made a slight error in my earlier post:

Should be:

Probability of 20% loss (= $800) = .15 times .80 = .12

Probability of 60% loss (=$2400) = .15 times .12 = .018

Probability of 100% loss (= $4000) = .15 times .08 = .012

Expected Loss = 800 times .12 + 2400 times .018 + 4000 times .012

= 96 + 43.20 + 48

= $187.20

Premium = $187.20