4. An amateur gardener with training in botany is experimenting with scientific crosspollination of pink irises with red, orange, and white irises. His annual experiments show that pink can produce 60% pink and 40% white, red can produce 40% red, 50%

pink, and 10% orange, orange can produce 25% orange, 50% pink, and 25% white, and white can produce 50% pink and 50% white.

(a) Express the gardener situation as a Markov chain.

(b) If the gardener started the cross-pollination with equal numbers of each type iris, what would the distribution be like after 5 years? In the long run?

(c) How many years on the average would a red iris take to produce a white bloom?