Question

Joey's sock drawer is unorganized and contains 3 black dress socks, 5 black ankle socks, 7 brown dress socks, and 6 brown ankle socks. What is the probability that Joey will blindly reach into his sock drawer and pull out a sock that is brown or a dress sock?

Answer 1

Joey has 21 socks all in all. Out of them, there are 10 dress socks and 13 brown socks. There are 7 brown dress socks. The probability,
                P (brown or dress) = P (brown) + P (dress) - P (brown and dress)
Substituting,
               P(brown or dress) = 13/21 + 10/21 - 7/21 = 16/21
Thus, the answer is 16/21.