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Roulette is a casino game that involves spinning a ball on a wheel that is marked...

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Statistics

Roulette is a casino game that involves spinning a ball on awheel that is marked with numbered squares that are red, black orgreen. Half of the numbers 1-36 are colored red and half are black.The numbers 0 and 00 are green. Each number occurs only once on thewheel.

We can make many different types of bets but the simplest areto bet on a number or on a color (either red or black). These arethe only two we will consider. After all the players place theirbets, the wheel is spun and the ball will land on a particularnumber and color.
We begin by placing a bet on a number between 1 and 36. Thisbet pays 36 to 1 in most casinos, which means that you will be paid$36 for each $1 you bet on the winning number. If you lose, yousimply lose whatever amount you bet.

1. Calculate the probability that you will win on a singlespin of the wheel.
2. Calculate the probability that you will lose on a singlespin of the wheel.
3. If you bet $8 on the winning number, how much money willyou win? What is the expected value of a bet on a single number ifyou bet $1. What if you bet 5 dollars? What if you bet 10 dollars?Do you see a pattern? Explain?



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