Multiple choice

Three symmetrical dice are thrown. The probability of obtaining a sum of $16$ points is

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{36}$
  3. $\dfrac{1}{216}$
  4. $\dfrac{1}{72}$
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B Correct answer
Explanation

Total outcomes = 6^3 = 216. Sum of 16 can be (6,6,4) in 3 ways, (6,5,5) in 3 ways. Total = 6 ways. Probability = 6/216 = 1/36.

AI explanation

The total number of outcomes when three symmetrical dice are thrown is 6 cubed, which equals 216. To obtain a sum of 16, the possible outcomes on the three dice are (5, 5, 6) and its different arrangements, along with (4, 6, 6) and its arrangements. There are 3 arrangements for (5, 5, 6) and 3 arrangements for (4, 6, 6), yielding 6 favorable outcomes. The probability is calculated as 6 / 216, which simplifies to 1/36.

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