A bag contains 3 red balls, 6 green balls, and 2 blue balls. Jack plays a game in which he bets $1 to draw a ball from the bag. If he draws a green ball, he wins $1 dollar; otherwise he loses a dollar. Assume that the balls are drawn with replacement and that Jack starts the game with $50 with the hope of reaching $100 before going bankrupt. What is the probability that he will succeed?