Multiple choice

A die is rolled three times. The probability that the sum of three numbers obtained is $15,$ is equal to :

  1. $ \dfrac {5}{108} $
  2. $ \dfrac {5}{216} $
  3. $ \dfrac {11}{216} $
  4. $ \dfrac {7}{108} $
  5. $ \dfrac {13}{216} $
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A Correct answer
AI explanation

The sample space for rolling a die three times has 6^3, or 216, outcomes. To get a sum of 15, the possible combinations of numbers are permutations of (4, 5, 6), (5, 5, 5), and (3, 6, 6). The number of permutations is 6 for (4, 5, 6), 1 for (5, 5, 5), and 3 for (3, 6, 6), giving 10 total favorable outcomes. Using the classical definition of probability, the result is 10/216, which simplifies to 5/108.

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