Question

Roulette is a casino game that involves spinning a ball on a wheel that is marked with numbered squares that are red, black or green. 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 the wheel.

We can make many different types of bets but the simplest are to bet on a number or on a color (either red or black). These are the only two we will consider. After all the players place their bets, the wheel is spun and the ball will land on a particular number and color.

We begin by placing a bet on a number between 1 and 36. This bet 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, you simply lose whatever amount you bet.

1. Calculate the probability that you will win on a single spin of the wheel.

2. Calculate the probability that you will lose on a single spin of the wheel.

3. If you bet $8 on the winning number, how much money will you win? What is the expected value of a bet on a single number if you bet $1. What if you bet 5 dollars? What if you bet 10 dollars? Do you see a pattern? Explain?

Answer 1

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