Multiple choice

Three dices are thrown simultaneously. The probability of getting a sum of $15$ is

  1. $\displaystyle \frac{5}{108}$
  2. $\displaystyle \frac{1}{72}$
  3. $\displaystyle \frac{5}{72}$
  4. $\displaystyle \frac{5}{36}$
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A Correct answer
Explanation

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

AI explanation

When three dice are thrown simultaneously, the total number of possible outcomes in the sample space is 6 times 6 times 6, which is 216. To get a sum of 15, the successful outcomes are the permutations of (4, 5, 6), (5, 5, 5), and (3, 6, 6). These give 6 plus 1 plus 3 favorable outcomes, totaling 10 ways. The probability is therefore 10 divided by 216, which simplifies to 5/108.

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