How do we find the integer corresponding to this probability problem?

Question

There are $n$ socks, $3$ of which are red, in a drawer. What is the value of $n$ if, when $2$ of the socks are chosen randomly, the probability that they are both red is $50\%$?

MY ATTEMPT

Unfortunately, I am having trouble to model correctly the problem. Could someone help me find the way to solve this exercise? Thanks in advance.

EDIT

This is my try. If we denote by $R$ the event "two red balls have been selected", we get \begin{align*} \mathbb{P}(R) = \frac{C(3,2)}{C(n,2)} = \frac{6}{n(n-1)} = \frac{1}{2} \Longleftrightarrow n^{2} - n - 12 = 0 \Longleftrightarrow n = 4 \end{align*}

I have done this before, but I committed some silly calculation mistakes. Anyway, thanks guys.

Answer 1

Hint: Try the problem backwards. Suppose you have $n$ socks, and $r$ red socks. If you pick two socks, what's the probability that both of them are red?