Two standard dice are thrown simultaneously. What is the probability that the sum of the two upper faces equals 8?

Introduction / Context:Rolling two fair six-sided dice yields 36 equally likely ordered pairs. We want the chance that the sum is exactly 8.

Given Data / Assumptions:

• Die outcomes are 1–6.
• Sample space size = 6 × 6 = 36.
• Sum target = 8.

Concept / Approach:Enumerate the pairs whose coordinates sum to 8 and divide by 36.

Step-by-Step Solution:Favorable pairs: (2,6), (3,5), (4,4), (5,3), (6,2) → 5 outcomes.Probability = 5 / 36.

Verification / Alternative check:Check neighboring sums: sums of 7 have 6 outcomes (symmetric peak), sums of 8 have 5, consistent with standard sum distribution.

Why Other Options Are Wrong:2/9 ≈ 8/36 (too large); 1/6 = 6/36 (wrong count); “Data Inadequate” is inappropriate since the model is standard.

Common Pitfalls:Forgetting that ordered pairs (3,5) and (5,3) are distinct outcomes.

Final Answer:5/36