SOLUTION: John is in a casino and decides to play some American roulette. First, he bets $1 on red and he wins. Next, he bets $1 on red again and he wins again. Use this information to answe

Question 1019396: John is in a casino and decides to play some American roulette. First, he bets $1 on red and he wins. Next, he bets $1 on red again and he wins again. Use this information to answer the following questions.

Based off American roulette with 38 slots: 18 red, 18 black, and 2 green.
wikipedia.org/wiki/Roulette#Bet_odds_table.
If John plays a third round and bets $1 on red, what is the probability that he will win a third time?

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

John's friend Sarah decides she wants to play 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?

Assume that both Sarah and John 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?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
the probability never changes with each time, and it will be 18/38 or 9/19.
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Here, the probability is (9/19)^3=0.1063
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This is the probability of winning all 3 times, 0.1063 PLUS
The probability of winning twice and losing once.
that probability is (9/19)(9/19)(10/19)=0.1181. This may happen 3 ways, so the probability of wining twice is 0.3543.
The overall probability, adding the 0.1063, is 0.4606.
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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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