9. At U of A, promotion from assistant to associate professor requires the equivalent of five years of seniority. Performance reviews are conducted once a year and the candidate is given either an average rating, a good rating, or an excellent rating. An average rating is the same as probation and the candidate gains no seniority toward promotion. A good rating is equivalent to gaining one year of seniorily, and an excellent rating adds two years of seniority. Statistics show that in any year 10% of the candidates are rated average, 70% are rated good, and the rest are rated excellent.

(a) Express the problem as a Markov chain.

(b) Determine the average number of years until a new assistant professor is promoted.