Question

Josh has 4 shirts (white, blue, green, and red) and 4 pairs of socks in the same colors. Suppose Josh grabs a shirt and a pair of socks without looking. What is the probability that his shirt and socks won't match?

Answer 1

First let us determine the total number of combinations that can be made from these pair. The number of combinations can simply be calculated by multiplication, so:

Combination = 4 * 4 = 16

Since we know that for each shirt color, there is a corresponding sock with the same color. So there are 4 matching pairs. Therefore the unmatching pairs are 12. Calculating the probability to get unmatching pair would be:

Probability of unmatching pair = 12/16 = 0.75

Interpretation: There is a 75% probability that his socks and shirt wont match.