wo tennis players A and B play according to the following rule: the first one to win two more sets than the other (2-0, 0-2, 3-1, 1-3, . . .) wins the match. From their previous matches, it is known that player A wins a set with a probability of 0.6. Modeling this match as a Markov chain, a. Give a finite state space and draw the state transition diagram. b. What is the probability that the player A wins the match? c. What is the expected number of sets played in the match?

Question

Two tennis players A and B play according to the following rule: the first one to win two more sets than the other (2-0, 0-2, 3-1, 1-3, . . .) wins the match. From their previous matches, it is known that player A wins a set with a probability of 0.6. Modeling this match as a Markov chain,
a. Give a finite state space and draw the state transition diagram.
b. What is the probability that the player A wins the match?
c. What is the expected number of sets played in the match?

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