Question

There are 11 clean individual socks in your sock drawer. There is only one matching pair among them. In the dark, you reach into the drawer and randomly pick 2 socks. What is the probability that you choose the matching pair? Write your answer as a fraction in simplest form.

The probability is:

Answer 1

The probability is: 1/55

Explanation:

The first sock you pick must be one of the two matching ones.

There are 2 matching socks out of 11, and all others are different.

First pick: p(one of the 2 matching socks) = 2/11

Now there are 10 socks left, and only one of them matches the first pick.

Second pick: p(the other matching sock) = 1/10

p(both matching socks) = 2/11 × 1/10 = 2/110 = 1/55