Suppose there are 10 different pairs of socks in a drawer. In other words, there are 20 singleton socks in total in the drawer. I randomly pick 2 socks out from the drawer. What is the probability that the 2 socks that I picked out is a matching pair?

My answer to this question is 1/2. But I am not sure if what I have done is correct because 1/2 seems quiteunbelievable.

My interpretation is this:

To get one particular pair of sock, I need this: $\displaystyle \frac{1}{20}\cdot\frac{1}{19}$

Since there are 20 socks in the drawer and I am picking 2 out of it, I take $\displaystyle \frac{1}{20}\cdot\frac{1}{19}\cdot\binom{20}{2} = \frac{1}{2} $.

But is this correct?