Whats the probability I roll a 2 on one of the dice if the sum rolled is 8? I have two dice and I want to find the probability of this situation:
Whats the probability I roll a 2 on one of the dice if the sum rolled is 8 ?
Is the answer $\frac{2}{36}$?

Consider it intuitively
We can draw a table to show this:
$$\begin{array}{|cc|cccccc|}\hline
&&&&&D_1\\
&&1&2&3&4&5&6\\
\hline
&1&2&3&4&5&6&7\\
&2&3&4&5&6&7&\color{red}8\\
D_2&3&4&5&6&7&\color{red}8&9\\
&4&5&6&7&\color{red}8&9&10\\
&5&6&7&\color{red}8&9&10&11\\
&6&7&\color{blue}8&9&10&11&12\\
\hline\end{array}$$
The numbers in red show where the sum is equal to $8$ and the blue number shows where one of the dice shows a $2$
Therefore we can see that we have a probability of $\dfrac15=\dfrac{\text{sum}=8\text{ and one dice showing }2}{\text{sum}=8}$
Now think mathematically
We can see that 
\begin{align}\frac15&=\frac{\frac 1{36}}{\frac5{36}}\\\\
&=\frac1{36}\div \frac{5}{36}\\
&= P(\text{sum}=8\text{ and one dice showing }2)\div P(\text{sum}=8)
\end{align}
