The federal government tries to boost small business activities by awarding annual grants for projects. All bids are competitive, but the chance of receiving a grant is highest if the owner has not received any during the last 3 years and lowest if awards were given in each of the last 3 years. Specifically, the probability of getting a grant if none were awarded in the last 3 years is .9. It decreases to .8 if one grant was awarded, .7 if two grants were awarded, and only .5 if 3 were received.

(a) Express the situation as a Markov chain.

(b) Determine the expected number of awards per owner per year.