Question

You have 6 brown socks and 4 black socks. You grab 2 socks in the dark at random. What is the probability of grabbing 2 socks that are the same color?

Answer 1

Let's start by assuming the first sock you pull out of the drawer is brown.

The probability that the sock you pull out is brown is 6/10 because there are 6 brown socks out of a total 10 socks in the drawer.

Once you pull this sock out, there are 9 total socks left and 5 brown socks left. So, your probability of choosing another brown sock is 5/9.

Now, you multiply these two fractions together in order to get the probability of pulling two brown socks out of the drawer.


You can do the same thing for the black socks except the probabilities change because you only start with 4 black socks. So, the probability of pulling out a black sock is 4/10.

Once you pull this sock out, the probability of pulling out another black sock is 3/9. In order to get the probability of pulling out two black socks. You now multiply those two fractions together.