What is the probability of rolling a sum of 7 with two dice?

Instruction: Assume two independent fair six-sided dice numbered 1–6. Calculate the probability of a sum of seven and explain why you count ordered pairs rather than equally likely sums.

Context: This question assesses the candidate's understanding of basic probability concepts and their ability to apply these concepts to a practical problem.

Updated

Official answer

Assume two independent fair dice numbered 1–6. There are 36 equally likely ordered outcomes. A sum of seven occurs for (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1).

Therefore P(sum = 7) = 6/36 = 1/6, about 16.67%. The pair (1,6) differs from (6,1) because the first and second dice are distinguished. The sums themselves are not equally likely: seven has six ways to occur, whereas two has only one.

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