A pair of dice is thrown. The probability that sum of numbers appearing on top faces is at most 10 is :
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
(d) $\dfrac{11}{12}$
Total outcomes = 36. Outcomes with sum more than 10 (i.e., sum 11 or 12): (5,6),(6,5),(6,6) = 3 outcomes. So P(sum ≤ 10) = $\dfrac{36-3}{36} = \dfrac{33}{36} = \dfrac{11}{12}$.
Source: Chapter 14, Section 14.1
Explanation
- "At most 10" means sum ≤ 10, so use the complement: find cases where sum > 10 (sum = 11 or 12), subtract from 36.
- Sum 11: (5,6),(6,5) → 2 outcomes; Sum 12: (6,6) → 1 outcome. Total = 3.
- P(sum ≤ 10) = 1 − 3/36 = 33/36 = 11/12. Option (d) is correct.