If you roll a pair of dice 100 times over the course of a game, what is the probability that you will have rolled doubles, at any point, exactly three times?

A roll of two dice is doubles with probability 6/36 = 1/6, so the probability of not rolling doubles is 5/6. For exactly 3 doubles in 100 rolls, use the binomial probability: C(100, 3)(1/6)^3(5/6)^97, which is approximately 0.0000156. The best answer is d, 0.0000156.

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