An urn contains red, green, and blue balls. Balls are chosen randomly with replacement

Chapter 4, Problem 52

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An urn contains red, green, and blue balls. Balls are chosen randomly with replacement (each time, the color is noted and then the ball is put back). Let r, g, b be the probabilities of drawing a red, green, blue ball, respectively (r + g + b = 1). (a) Find the expected number of balls chosen before obtaining the first red ball, not including the red ball itself. (b) Find the expected number of dierent colors of balls obtained before getting the first red ball. (c) Find the probability that at least 2 of n balls drawn are red, given that at least 1 is red.

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