. Jones plays a new game every day. If Jones wins a game, then she wins the next one with probability .6; if she has lost the last game but won the one preceding it, then she wins the next with probability .7; if she has lost the last 2 games, then she wins the next with probability .2.

(a) Define a Markov chain having 3 states that can be used to analyze the preceding. Give its transition probability matrix.

(b) What proportion of games does Jones win