When a pair of six face fair dice are thrown, the probability that the sum of the numbers on the two dice is greater than 7 is

The random experiment is tossing two dice at a time

Let $S$ be the sample space, $n\left(S\right)=6^2=36$

Let $A$ be the event of getting numbers whose sum is more than 7

$$\begin{gathered} A=\left\{\left(2,6\right),\left(3,5\right),\left(3,6\right),\left(4,4\right),\left(4,5\right),\left(4,6\right),\left(5,3\right),\left(5,4\right), \\ \left(5,5\right),\left(5,6\right),\left(6,2\right),\left(6,3\right),\left(6,4\right),\left(6,5\right),\left(6,6\right)\right\} \end{gathered}$$

Hence, $n\left(A\right)=15$

Therefore, $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\boxed{\frac{15}{36}}$