Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers shown is 11?

Introduction / Context:When two dice are rolled, there are 36 equally likely ordered outcomes. We identify those with sum 11 and divide by 36.

Given Data / Assumptions:

• Ordered pairs (d1, d2) with d1, d2 ∈ {1..6}.
• Each pair equally likely with probability 1/36.

Concept / Approach:Find all pairs (x, y) such that x + y = 11.

Step-by-Step Solution:Pairs summing to 11: (5,6) and (6,5) → 2 favourable outcomes.Probability = 2/36 = 1/18.

Verification / Alternative check:Neighbouring sums: 10 has 3 pairs; 12 has 1 pair. The count for 11 (=2) fits the symmetric distribution of sums.

Why Other Options Are Wrong:1/6 implies 6 favourable outcomes; 1/9 implies 4; 1 is impossible for a specific sum event.

Common Pitfalls:Forgetting ordered pairs are distinct; (5,6) and (6,5) are different outcomes.

Final Answer:1/18