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.
Doubles 3 Times 21973F
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