Teddy has a two pairs of black shoes and three pairs of brown shoes. He also has three pairs of red socks, four pairs of brown socks and six pairs of black socks.

If Teddy chooses a pair of shoes at random and a pair of socks at random, what is the probability that he chooses shoes and socks of the same color?

A. 4/13
B. 24/65
C. 6/13

Correct Answer: B

He has 5 pairs of shoes altogether and 13 pairs of socks altogether. Therefore:

P (He chooses black shoes) = 2/5
and P(He chooses brown shoes) = 3/5
P(He chooses red socks) = 3/13 and P(He chooses brown socks) = 4/13 and P(he chooses black socks) = 6/13.

The tree diagram looks like this:

Therefore P(He chooses shoes and socks of the same color) = 12/65 + 12/65 = 24/65