Rachel and annah play each other at badminton. each games results in either a win for Rachel or a win for Annah, the P of rach winning the first game is 0.6, If rach wins the first game the prob of her winning the next game is 0.7 but if she loses the P is 0.4

Find conditional prob that rach wins the first game given that she loses the second one....

so P (AUB) = wins 1st and loses second... = 0.6 x 0.3 = 0.18

And prob she wins the first game = 0.6

So the Conditional prob = 0.18/0.6 = 0.3 ?

The answer is 0.429 ?

Help ?

and second part, find P that rachel wins 2 games and loses 1 game out of the first free games she plays ?

the p of only 2 match is given ? :s all confused...