In tennis, when the score becomes 40-40, it is called 'deuce. Once at deuce, a plyer must win two consecutive points to win the game. Suppose that two players A and B just arrived at the 'deuce' score. These two players are equally likely to win a point per play. Consider a Markov Chain to describe the game status. a. Define the state space. (Hint: use the difference of the players' points.) b. Write the one-step transition probability matrix. c. How many classes are in the Markov Chain? (Make sure to provide explanation.) d. Identify each of the following states. Recurrent States: Transition States: Absorbing States:
