There are 18 total socks in the drawer, and 2 of them are black. There are two ways to draw mismatched socks: he can draw a black sock on the left foot and a white sock on the right foot, or he can draw a white sock on the left foot and a black sock on the right foot.
The probability of drawing a black sock on the left foot and a white sock on the right foot is 2/18⋅16/17=8/153.
The probability of drawing a white sock on the left foot and a black sock on the right foot is also 8/153.
So, the probability of drawing mismatched socks is 8/153+8/1538=16/153.
