The Expected Value of a Roulette Wheel

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One common type of roulette wheel has 38 slots—18 red, 18 black, and 2 green. The 36 red and black slots are numbered 1 to 36. The green slots are numbered 0 and 00. As the wheel is spun, a small white ball is placed on the wheel, eventually stopping in one of the slots. Suppose you place a $1 bet on the number 19. If your number comes up, the casino pays you $35 and you also keep your $1 bet; otherwise, you lose your dollar. What is the expected value of this bet?

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The Expected Value of a Roulette Wheel