replacement value

Question

Assume that you have a car worth
$ 6 650
 and you wish to insure it for its full replacement value if it is stolen. If there is a
1% chance that the car will be stolen, what would a fair premium price be?

Answer 1

This is an expected value question but it is missing a key piece of information which is what is period over which the probability of the car being stolen is 1%? Is it over the insured lifetime of the car or annually? 

 

In any case, I'll assume that it's 1% probability over the course of 1 year that the car will be stolen. In that case, the expected value of the payout from the insurance company would be 0.01*6650 = $66.50 per year. So that would be a breakeven annual premium for the insurance company.