# Probability Problem

• Oct 8th 2006, 03:47 PM
JaysFan31
Probability Problem
Could someone help me set-up the following problem?

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 has 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 \$12,000 car so that the expected gain by the company is zero?

Thanks for any help.
• Oct 8th 2006, 09:21 PM
CaptainBlack
Quote:

Originally Posted by JaysFan31
Could someone help me set-up the following problem?

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 has 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 \$12,000 car so that the expected gain by the company is zero?

Thanks for any help.

The expected loss to the company is

0 with probability 0.85 (no accident)

0.15*0.8*0.2*12000 (accident, 20% market value damage)

0.15*0.12*0.6*12000 (accident, 60% market value damage)

0.15*0.08*12000 (accident, 100% market value damage)

This totals:

C=0.15*15000*(0.8*0.2 + 0.6*0.12 + 0.08) = 561.6.

So the company needs to charge \$561.6 for the expected gain to be zero.

RonL