J plays a new game every day. If J wins a game, then she wins the next one with probability 0.6; if she has lost the last game but won the one preceding it, then she wins the next with probability 0.7; if she has lost the last 2 games, then she wins the next with probability 0.2.

(a) What proportion of games does J win?

(b) Suppose J has been playing a long time. If J loses her game on Monday, what is the probability she will win on Tuesday?