Multiple choice

Three identical dice are rolled. The probability that the same number will appear on each of them is

  1. $\displaystyle \frac { 1 }{ 6 } $
  2. $\displaystyle \frac { 1 }{ 18 } $
  3. $\displaystyle \frac { 1 }{ 36 } $

  4. None of these
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C Correct answer
Explanation

Total outcomes = 6 * 6 * 6 = 216. Favorable outcomes (same number) = (1,1,1), (2,2,2), ..., (6,6,6) = 6. Probability = 6 / 216 = 1 / 36.

AI explanation

Assuming the question treats the dice as distinct due to standard probability rules, the total number of outcomes is 6 * 6 * 6 = 216. For all three dice to show the same number, there are only 6 favorable outcomes (1,1,1), (2,2,2), (3,3,3), (4,4,4), (5,5,5), and (6,6,6). The probability is 6/216, which simplifies to 1/36.

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