Three fair dice are thrown simultaneously. What is the probability that the sum of the numbers obtained on the three dice is 16?

Question

Three fair dice are thrown simultaneously. What is the probability that the sum of the numbers obtained on the three dice is 16?

1. A. 1/36 (Correct answer)
2. B. 5/216
3. C. 1/54
4. D. 1/72

Correct Answer

Option A — 1/36

Detailed Solution & Explanation

The correct answer is 1/36.

Key Points

• Three dice give 6³ = 216 equally likely outcomes.
• A total of 16 arises in only two number combinations: (6, 6, 4) and (6, 5, 5).
• Each has one repeated value, so each yields 3!/2! = 3 arrangements.
• Favourable outcomes = 3 + 3 = 6, so the probability = 6/216 = 1/36.

Additional Information

• The distractor 5/216 comes from missing one of the six arrangements.
• Sum 16 is symmetric with sum 5 (since 21 − 16 = 5), and sum 5 likewise has 6 outcomes — a useful symmetry check for three dice, where totals are symmetric about 10.5.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*