Alice, Bob, and Chuck are three students who go out for coffeeevery day. But every day, they randomly determine who pays for thethree coffee. If Alice pays for the coffee today, then there is a25% chance she will also pay tomorrow, a 50% chance Bob will paytomorrow, and 25% chance Chuck will pay tomorrow. If Bob paystoday, there is a 50% chance Alice will pay tomorrow, and 50%chance Chuck will pay tomorrow. If Chuck pays today, there is a 50%chance Alice will pay tomorrow, 25% chance Bob will pay tomorrow,and 25% chance that Chuck will pay again tomorrow. a. This is aMarkov chain. What are the three states? b. Calculate whatproportion of time each person will pay over the long term
