Subjects probability

Doubles 3 Times 21973F

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1. **Problem Statement:** Two standard dice are rolled. Find the probability that you roll doubles 3 times in a row. 2. **Formula and Rules:** The probability of rolling doubles on one roll of two dice is the number of doubles outcomes divided by total outcomes. - Total outcomes when rolling two dice: $6 \times 6 = 36$ - Doubles outcomes: $(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)$, so 6 outcomes. Therefore, probability of doubles in one roll is: $$P(\text{doubles}) = \frac{6}{36} = \frac{1}{6}$$ 3. **Rolling doubles 3 times in a row:** Since each roll is independent, multiply the probabilities: $$P(\text{doubles 3 times}) = \left(\frac{1}{6}\right)^3 = \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} = \frac{1}{216}$$ 4. **Final answer:** $$\boxed{\frac{1}{216}}$$ This means the chance of rolling doubles three times consecutively is one in two hundred sixteen.