Conditional probability!

There are 11 equally likely outcomes given that at least one of the dice shows a $2$ : $\begin{array}{cc} \text{Die 1} & \text{Die 2} \\ 1 & 2 \\ 2 & 1 \\ 2 & 2 \\ 3 & 2 \\ 2 & 3 \\ 4 & 2 \\ 2 & 4 \\ 5 & 2 \\ 2 & 5 \\ 6 & 2 \\ 2 & 6 \\ \end{array}$ Of these options, only two (2 & 5 and 5 & 2). Thus the answer is $\boxed{\frac{2}{11}}$ .

Probability of a sum of 7 and a 2 on either, i.e. a 2 and a 5. = 2/36

Probability of a 2 on either = 1/6 +1/6 -1/36=11/36

Therefore, the answer is the ratio of these two = 2/11