Your friend in a casino for the first time and he decides to play some American
ID: 3256250 • Letter: Y
Question
Your friend in a casino for the first time and he decides to play some American roulette. First, he bets $10 on red and he wins! Then, he bets $10 on red again and he wins again! Use this information to answer the following questions. Note that this is American roulette with 38 slots: 18 red, 18 black, and 2 greens. A. If your friend plays a third round and bets $10 on red, what is the probability that he will win that round? B. If an individual plays three rounds of American roulette, what is the probability that he or she will win all three times? C. Your friend's friend joins him at the casino and she plays 3 games of roulette, betting $10 on red each time. What is the probability that she will finish with more money than she started with? D. Assume that both of these individuals 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.Explanation / Answer
Solution:
A red bet has the probability of
P(R) = 18/38 = 9/19
a) The probability of each spin is independent of previous results.
P(R) = 9/19
b) P(RRR) = (9/19)^3 = 729/6859
c) The payout on winning is 1:1 on red. So you win $100 if you bet $100. Let's look at her expected winnings for one hand and multiply it by 3.
E = 9/19 *10 - 10/19*10 = -10/19
So she should expect to lose $0.526 each time, in 3 hands $1.578.
d) 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. So long as the overall probability of the casino's winning is greater than 50%, over the long run the casino will make money, even if several people in a row make money. Not only will the casino make money, but over a period of time, the amount they will make can be predicted to a very high degree of accuracy.
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