Question

In the the casino game of roulette, players make bets based on a wheel with 38 numbered pockets (18 red pockets, 18 black pockets, and two green pockets, labeled 0 and 00). The wheel is then spun one direction and the ball is spun in the opposite direction. Eventually, the ball will land in one of the numbered pockets. The wheel is designed so that the ball has an equal chance of landing in any one of the pockets.

Suppose you play roulette 10 times, making a single number bet each time. What is the probability that you would win 3 times within those 10 plays, to three decimal places? Hint: this is a binomial distribution problem.

This probability problem I have missed twice on my business analysis homework and have only one more try. Please help me step by step. Thanks a lot for the assistance.

Answer 1

Number of pockets = 38

Probability of winning a single number bet : p= 1/38

q = 1- p= 1-1/38 = 37/38

Number of trails : Number of times played : n =10

X : Number of wins

X follows a Binomial distribution with n=10 and p=1/38 (q=37/38) with probability distribution

Probability of winning 'r' times is given by

Probability that you would win 3 times within those 10 plays = P(X=3)

Probability that you would win 3 times within those 10 plays = 0.002