A player plays a roulette game in a casino by betting on a single number each time. Because the wheel has 38 numbers, the probability that the player will win in a single play is 1/38. Each play of the game is independent of all previous plays.
a. Find the probability that the player will win for the first time on the 10th play.
b. Find the probability that it takes the player more than 50 plays to win for the first time.
c. A gambler claims that because he has 1 chance in 38 of winning each time he plays, he is certain to win at least once if he plays 38 times. Does this sound reasonable to you? Find the probability that he will win at least once in 38 plays.