Probability of $2$ people being together out of a group of $4$. There were $2$ people who wanted to be in a group together. Those $2$ people were in a pool of $4$ people. Someone would randomly select $2$ people in a row and those people would be in a group together. The remaining $2$ would also be in a group. 
What the probability of those $2$ people who wanted to be in the same group actually being in the same group?
What I tried
Lets assume that the $2$ who want to be together are person A and B respectively and person C and D are the other $2$.
The probability of choosing person A and B is $\dfrac 14 \cdot \dfrac 13 = \dfrac 1{12}.$

We are placing the four people in two groups of two people.  Notice that person $A$ must be in a group with one of the other three people, of whom only one is person $B$.  Hence, the probability that persons $A$ and $B$ are placed in the same group is $1/3$. 
