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14. The casino game of American Roulette consists of a circular wheel with 38 spots. Thirty six of the spots are numbered 1, 2, 3, .., 36. Eighteen of these numbers are colored black and the other eighteen are colored red. The remaining two spots are colored green with no number assignment. If you play a color (either red or black), the casino will pay you even odds. That is, if you play black and wager 1 dollar, you will profit 1 dollar if black comes up on that particular spin of the wheel. (a) Let Xprofit or loss for one spin of the wheel when playing black. Find the expected value of X and explain what it means. Answer: $-2/38 (b) How much money is expected to be won or lost after 1,000 games where the player wagers 10 dollars per game on black? Answer: expect to lose $526.32(4.2.2)

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