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jmc

prealgebra intermediate

Problem

Suppose we have 2 fair 6-sided dice numbered from 1 to 6. If we roll them both, what is the probability that the two numbers shown sum to 7?
Solution
There are 6 equally likely outcomes for each die, so there are total equally likely outcomes for both dice together. The outcomes which sum to 7 are: 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, and 6 + 1, for a total of 6 equally likely successful outcomes. Therefore, the probability of rolling a sum of 7 is .
Final answer
\frac{1}{6}