The question is shown below. It mainly focus on Markov chain.

gives a probabilty of no craters within it which is 0.9. 5. (25%) In tennis, a game often reaches the state of "deuce" where the two players are tied and one player must win two points in a row in order to win the game. Suppose that, for any point being played, Player 1 wins with probability 0.6 and Player 2 wins with probability 0.4. The progress of the game starting with "deuce" can be modeled as a discrete-time Markov chain. (2) Draw a state transition diagram for this Markov chain clearly showing all transition probabilities. The Markov chain should include the states indicating that Player 1 wins and that Player 2 wins. (22) For each state in the Markov chain, indicate whether it is transient, positive recurrent or null recurrent. (22i) Suppose the game is at a state where Player 2 has won a point after "deuce". Determine the probability that Player 1 wins the game