5 Rachel and Anna play each other at badminton. Each game results in either a win for Rachel or a win for Anna. The probability of Rachel winning the first game is 0.6 . If Rachel wins a particular game, the probability of her winning the next game is 0.7 , but if she loses, the probability of her winning the next game is 0.4 . By using a tree diagram, or otherwise,

1. find the conditional probability that Rachel wins the first game, given that she loses the second,
2. find the probability that Rachel wins 2 games and loses 1 game out of the first three games they play.