Two players A and B are playing the following game. There is an urn containing 4 red, 3 yellow and 2 white balls. First, player A draws three balls without replacement and wins the game if the balls she draws have three different colors. Otherwise, she puts the balls back and player B repeats the same with the same conditions of winning. They keep going until there is a winner.

a) What is the probability that A wins the game on her first draw?

b) What is the probability that A wins the game?

c)Suppose they toss a fair coin to see who starts the game with HEADS favoring A. What is the probability that the outcome of the toss was heads, given that B wins the game?

d) If they play the game until someone wins three times, what is the probability that A wins given that B starts every time?