Sum of Seven

Question

You roll two fair six-sided dice. What is the probability that the sum is exactly 7? Give your answer as a fraction or decimal.

Accepted Answer

There are 36 equally likely ordered outcomes. The pairs summing to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) , exactly 6 of them, and notably 7 is the only total that can be completed from any first roll. So P(textsum=7) = frac636 = frac16 approx 0.1667. Why interviewers ask it 7 is the modal sum of two dice. Knowing the full distribution (counts 1,2,3,4,5,6,5,4,3,2,1 for sums 2 through 12) lets you instantly price dice games and is assumed knowledge for harder questions.

Sum of Seven

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