Math GRE - #3

A drawer contains 2 blue, 4 red, and 2 yellow socks. If 2 socks are to be randomly selected from the drawer, what is the probability that they will be the same colour?

• $\frac{2}{7}$
• $\frac{2}{5}$
• $\frac{3}{7}$
• $\frac{1}{2}$
• $\frac{3}{5}$

The probability of getting 2 blue in a row is: $\frac{2}{8}\frac{1}{7}=\frac{1}{28}$.

The probability of getting 2 yellow in a row is: $\frac{2}{8}\frac{1}{7}=\frac{1}{28}$.

The probability of getting 2 red in a row is: $\frac{4}{8}\frac{3}{7}=\frac{6}{28}$.

So the total probability is: $$\frac{1}{28}+\frac{1}{28}+\frac{6}{28}=\frac{2}{7}.$$