SOLUTION: Mr. Z is in a casino for the first time! He decides to play some American roulette. First, he bets $1 on red and he wins! Then, he bets $1 on red again and he wins again! A. If

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Question 1020068: Mr. Z is in a casino for the first time! He decides to play some American roulette. First, he bets $1 on red and he wins! Then, he bets $1 on red again and he wins again!
A. If Mr. Z plays a third round and bets $1 on red, what is the probability that he will win a third time?

B. If an individual plays three rounds of American roulette, what is the probability that he or she will win all three times?

C. Mr. Z�s friend, Ms. Y, joins him at the casino and she plays 3 games of roulette, betting $1 on red each time. What is the probability that she will finish with more money than she started with?

D. Assume that both Mr. Z and Ms. Y made money during their first short trip to the casino. How are casinos making money if two people can walk in and come out with more money? Apply what you have learned about probability distributions in this lesson. It is expected that about 50-75 words will be needed to fully answer this question.

Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
In American roulette, there are 38 bins, 18 red, 18 black, 0 and 00 (both green).
A red bet has the probability of

a) The probability of each spin is independent of previous results.

b)
c) The payout on winning is 1:1 on red. So you win $1 if you bet $1. Let's look at her expected winnings for one hand and multiply it by 3.

So she should expect to lose 5.3 cents each time, in 3 hands 15.7 cents.
d) As you see from c), although people can and do win big occasionally on average and over time, the casino will win, slowly but surely. Otherwise they wouldn't be in business. You can fill in with additional words.