There is $n$ pairs of socks that each sock having one mate,each pair is different from another pair .
There is $2$ drawers: left drawer and right drawer.
All the left socks are in the left drawer and all the right socks are in right drawer.
Every day I take $1$ sock from the left drawer and $1$ sock from the right drawer.
The socks are worn at that day and then thrown into a laundry basket,so after $n$ days the drawers will be empty.
What is the probability that in day number $k$ , I took a matching pair,when $1\le k \le n$ ?
I want to find the probability that a match occurs on day $k$?
How do I approach to that type of question?