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Roulette is a very popular casino game, especially in Europe. The Roulette Wheel

ID: 3175134 • Letter: R

Question

Roulette is a very popular casino game, especially in Europe. The Roulette Wheel in Europe has 37 pockets. They are numbered 0, 1, 2, ..., 36 (see the picture below). On each spin of the wheel, a ball lands in a pocket, and each pocket is equally likely. The "0" is a green-colored pocket and all the rest are either red or black. The casino payout for a bet on "red" is 1:1 (meaning for $1 bet, you will receive back your $1 plus $1 from the casino). You bet $1 on red for one spin. Construct a probability distribution for your profit and find the expected value. In Craps, people bet on the sum of two fair, 6-sided dice. A bet on the roll of 2, 3, or 12 is called a "craps". The payout for "craps" is 7:1. This means that if you bet $1 and win, you will receive your Si back plus $7 from the casino. You decide to bet $1 on "craps". Fill in the probability distribution for your profit. Find the expected value of your profit. Is this a fair game? Explain.

Explanation / Answer

As multiple questions are posted, only the first one will be answered.

5. Number of green = 1

Number of reds = (37-1) / 2 = 18

P(Win) = 18/37

P(Lose) = 1 - 18/37 = 19/37

On winning, profit = -1 + 2 = 1

On losing, profit = -1 + 0 = -1

Probability distribution of profit X:

Expected value = 1*(18/37) + (-1)*(19/37) = -1/37 = -0.0270

X P(X) 1 18/37 -1 19/37