The Big Six Wheel (or Wheel of Fortune) is a casino and carnival game that is well known for being a big money maker for the casinos. The wheel has 54 equally likely slots (outcomes) on it. The slot that pays the largest amount of money is called the joker. If a player bets on the joker, the probability of winning is 1/54. The outcome of any given play of this game (a spin of the wheel) is independent of the outcomes of previous plays.
a. Find the probability that a player who always bets on joker wins for the first time on the 15th play of the game.
b. Find the probability that it takes a player who always bets on joker more than 70 plays to win for the first time.