Two standard dice are rolled. What is the probability that the sum of the two numbers is at least 8?

Step-by-step solution

1. Total possible outcomes when rolling two dice = 6 × 6 = 36.
2. Count favourable outcomes for sums 8,9,10,11,12.
3. For sum 8: 5 combinations; 9: 6; 10: 5; 11: 4; 12: 3.
4. Total favourable = 5+6+5+4+3 = 23.
5. Probability = favourable/total = 23/36.

Concept tested: Discrete random variables – dice sum probability.

Published 29 August 2026 · How this solution was prepared and checked

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