Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is $7$?

The total sample space has $6 \times 6 = 36$ outcomes. The pairs that sum to 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), which is 6 favourable outcomes. So $P(\text{sum}=7) = \dfrac{6}{36} = \dfrac{1}{6}$. Useful fact: 7 is the most likely sum when rolling two dice. The probability distribution of the sum is symmetric around 7 and drops off toward 2 and 12.