Question

Consider the game of tennis when deuce is reached. If a player wins the next point, he has advantage. On the following point, he either wins the game or the game returns to deuce. Assume that for any point, player A has probability 6 of winning the point and player B has probability 4 of winning the point.

(a) Set this up as a Markov chain with state 1: A wins; 2: B wins; 3: advantage A; 4: deuce; 5: advantage B
(b) Find the absorption probabilities
(c) At deuce, find the expected duration of the game and the probability that B will win.

Answer 1

Please see attachment

Explanation:

Please note that an assumption is that for any point, player A has probability 0.6 of winning the point and player B has probability 0.4 of winning the point.

Please see attachment for an explanation .