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)
This solution provides the answer to the probability problem. Supplementary examples are also provided.