A jar contains 11 red marbles, 12 blue marbles, and 6 white marbles. Four marbles from this jar are selected, with each marble being replaced after each selection. What is the standard deviation of X, the number of draws until the first red marble?

The probability of drawing a red marble on any draw is 11/29, and replacement makes the draws independent. Thus X follows a geometric distribution, whose standard deviation is √(1 − p)/p. Substituting p = 11/29 gives √(18/29)/(11/29) ≈ 2.0770, so the answer is C, 2.0770.

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