A drawer has 10 red socks and 10 blue socks. If 3 socks are selected from the drawer, without replacement, what is the probability that they will all be the same color?
A) 0.3000
B) 0.0225
C) 0.1500
D) 0.2105
E) 0.1667

Question

Quizplus · Accepted Answer

The total number of ways to select 3 socks from 20 is (20 choose 3) = 1140.

To select 3 socks all of the same color, either all 3 red or all 3 blue, there are (10 choose 3) + (10 choose 3) = 240 + 240 = 480 ways.

Thus, the probability of selecting 3 socks all of the same color is 480/1140 = 0.2105.

Therefore, the best choice is D.

A Drawer Has 10 Red Socks and 10 Blue Socks