Alice, Bob, and Chuck are three students who go out for coffee every day. But every...

Alice, Bob, and Chuck are three students who go out for coffee every day. But every day, they randomly determine who pays for the three coffee. If Alice pays for the coffee today, then there is a 25% chance she will also pay tomorrow, a 50% chance Bob will pay tomorrow, and 25% chance Chuck will pay tomorrow. If Bob pays today, 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 a Markov chain. What are the three states? b. Calculate what proportion of time each person will pay over the long term

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