If I follow the question:
You are asked to find .
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 ?
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...
The first part the answer is 0.429, and the way i learnt conditional probability is, P(A U B)/A....
And for the second part, that leaves me some choices i think, like she wins first, then loses second and wins third,
and etc etc, so could be a combination ?