From past experience, an automobile insurance company knows that a given automobile will suffer a total loss with probability .02, a 50% loss with probability .08, or a 25% loss with probability .15 during a year. What annual premium should the company charge to insure a $10,000 automobile, if it wishes to "break even" on all policies of this type? (Assume there will be no other partial loss)
$10,000 .02 (represents a total loss)
$5,000 .08 (represents a 50% loss)
This solution provides the answer to the probability problem. Supplementary examples are also provided.