First, the probability of winning a game is: .
Second, for his $6 bet, he gets to play three
I assume that if he wins, he stops playing.
There are three ways he can.
Win on the 1st try: .
Win on the 2nd try: .
Win on the 3rd try: .
but wait, aren't there many possibilities on how to win on the second try? One possibility, roll the die & don't get 4 (you lost so second try) then roll the die and get 4, then draw 2 jokers. Second possibility roll die and get 4, then don't draw 2 jokers (you lost so second try), roll 4, then draw 2 jokers? which results in two different probabilities of winning on the second attempt. can you apply the geometric distribution equation? :s