Question: Capa plays either one or two chess games every day, with the number of games that she plays on successive days being a Markov chain

Capa plays either one or two chess games every day, with the number of games that she plays on successive days being a Markov chain with transition probabilities

P1,1 = 0.2, P1,2 = 0.8, P2,1 = 0.4, P2,2 = 0.6.

Capa wins each game with probability p. Suppose she plays two games on Monday.

(a) (2 marks) What is the probability that she wins exactly one game on Tuesday?

(b) (3 marks) What is the expected number of games that she plays on Wednesday?

Below is my own solution. Please verify if they are correct. I'm not too sure about the last question. Thank you!

Capa plays either one or two chess games every day, with the

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