Kevin is trying to find a white sock in his drawer. He has 16 white socks, 4 brown socks, and 6 black socks. What is the probability that he pull out either a black or brown sock, puts it back, and then pulls out a white sock?

A) 9/13

B) 20/13

C) 40/169

D) 96/169

We have to assume that he does all this with his eyes closed, and so his selections are completely random.

- - There are 26 socks in the drawer all together.

- - 10 of them are black or brown.

- - So the probability that he pulls out

either a black sock or a brown one is

10/26 = 5/13 = about 38.5%.

- - He puts it back, so there are still 26 socks in the drawer.

- - 16 of them are white.

- - So now, the probability of pulling out a white one is

16/26 = 8/13 = about 61.5%.

The probability of the whole process happening

just exactly as you described it is

(10/26) x (16/26)

= (5/13) x (8/13)

= (40) / (13²) = 40/169 = about 23.7%.

Quick check:

We got 38.5% the first time, and 61.5% the second time.

(38.5%) x (61.5%)

= (0.385 x 0.615)

= 0.2367 = = > 23.7% < = = yay! that's good enough for me