Multiple choice

Four dice are thrown simultaneously. Find the probability that all of them show the same faces.

  1. $\dfrac {1}{216}$
  2. $\dfrac {15}{16}$
  3. $\dfrac {15}{36}$
  4. $\dfrac {1}{2}$
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A Correct answer
Explanation

Total outcomes for 4 dice = 6^4 = 1296. Favorable outcomes (all same) are (1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6), which is 6. Probability = 6/1296 = 1/216.

AI explanation

When four dice are thrown, the total number of possible outcomes is 6^4, which equals 1296. The number of favorable outcomes where all dice show the same face is 6, corresponding to the outcomes (1,1,1,1), (2,2,2,2), and so on up to 6. By dividing the favorable outcomes by the total outcomes, we get the probability as 6 / 1296, which simplifies to 1 / 216.

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