5) A player plays a roulette game in a casino by betting on a single number each

Question

5) 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 10h play. b) Find the probability that it takes the player more than 50 plays to win the first game. c) The 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. Find the probability that he wil win at least once im 38 play

Explanation / Answer

Probability that player will win in a single play is 1/38

a)

Probability that player will win for the first time on the 10th play = Probability that player will lose first 9 plays and wins the 10th 1/38)9(1/38) = 0.0207

b)

probabilty that it takes more than 50 plays to win the first game =  Probability that player will lose the first 50 plays

= (1- 1/38)50 = 0.2636

c)

probability that he will win at least once in 38 plays = 1 - probability that he will loose all 38 games = 1 - (1-1/38)38

= 1 - (37/38)38 = 0.637

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