# A man has five pairs of socks of which no two pairs are the same color. He randomly selects two socks from the drawer. What is the probability that he gets a matched pair?

Apr 2, 2017

See the entire explanation below:

#### Explanation:

Because the man has five pairs of socks the man therefore has 10 socks altogether.

When the picks the first sock, there are 9 socks remaining in the drawer. 1 of the socks is the same color as the sock he selected, the other 8 socks are of a different color.

When the man randomly selects the next sock the man has a 1 in 9 chance of picking a sock of the same color as the first sock he selected.

Therefore the probability of the man getting a matched pair is:

$\frac{1}{9}$ or 11.1%