Question:
Three identical fair dice are rolled. The probability that the same number appears on each of them is
Three identical fair dice are rolled. The probability that the same number appears on each of them is
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For identical outcomes across trials, count matching cases directly.
Updated On: Apr 30, 2026
- \(1/3\)
- \(1/6\)
- \(1/36\)
- \(1/216\)
- \(1/9\)
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The Correct Option is C
Solution and Explanation
Concept:
Probability = Favorable outcomes Total outcomes.
Step 1: Total outcomes. Each die has 6 outcomes: \[ 6 \times 6 \times 6 = 216 \]
Step 2: Favorable outcomes. Same number on all dice: \[ (1,1,1),(2,2,2),\dots,(6,6,6) \] Total = 6 outcomes
Step 3: Compute probability. \[ \frac{6}{216}=\frac{1}{36} \]
Step 1: Total outcomes. Each die has 6 outcomes: \[ 6 \times 6 \times 6 = 216 \]
Step 2: Favorable outcomes. Same number on all dice: \[ (1,1,1),(2,2,2),\dots,(6,6,6) \] Total = 6 outcomes
Step 3: Compute probability. \[ \frac{6}{216}=\frac{1}{36} \]
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