Multiple choice

Three identical dice are thrown. What is the probability of getting a total of $15$?

  1. $\cfrac{3}{108}$
  2. $\cfrac{4}{108}$
  3. $\cfrac{5}{108}$
  4. $\cfrac{6}{108}$
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C Correct answer
Explanation

Total outcomes for 3 dice = 6^3 = 216. Combinations for sum 15: (6,6,3)x3, (6,5,4)x6, (5,5,5)x1 = 3 + 6 + 1 = 10. Probability = 10/216 = 5/108.

AI explanation

When three dice are thrown, the total number of outcomes in the sample space is 6*6*6 = 216. To obtain a total of 15, the possible permutations are (6,6,3), (6,5,4), and (5,5,5), which give 3, 6, and 1 arrangements respectively, for a total of 10 favorable outcomes. The probability is therefore 10/216, which simplifies to 5/108.

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