Payoff Insurance Company charges a customer according to his or her accident history. A customer who has had no accident during the last two years is charged a $100 annual premium. Any customer who has had an accident during each of the last two years is charged a $400 annual premium. A customer who has had an accident during only on of the last two years is charged an annual premium of $300.
A customer who has had an accident during the last year has a 10% chance of having an accident during the current year. If a customer has not had an accidnet during the last year, there is only a 3% chance that he or she will have an accident during the current year. During a given year, what is the average premium paid by a Payoff customer? (hint: In case of difficulty, try a four-state Markov chain)