A pair of dice is rolled. What is the probability that their sum to 7 given that neither die shows a 2 ?

$A$  be the event of getting sum 7 when two dies are rolled

$B$ be the event of neither die shows 2

$n\left(B\right){=}^5{C}_1{\cdot }^5{C}_1\mathrm{\&}n\left(S\right)=36\Rightarrow P\left(B\right)=\frac{25}{36}$

$A\cap B$ is the event of both sum 7 neither die shows 2

$A\cap B=\left\{\right(6,1\left)\right(1,6\left)\right(4,3\left)\right(3,4\left)\right\}\Rightarrow n(A\cap B)=4$

$P(A\cap B)=\frac{n(P\cap B)}{n\left(s\right)}=\frac{4}{36}$

$P(A/B)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{4}{{\displaystyle \frac{\frac{36}{25}}{36}}}=\frac{4}{25}$