Question

Teddy has two pairs of black shoes and three pairs of brown shoes. He also has one pair of brown pants and three pairs of black pants. Teddy has two pairs of red socks, four pairs of brown socks and six pairs of black socks. If Teddy chooses a pair of shoes at random, a pair of pants at random, and a pair of socks at random, what is the probability that he chooses shoes, pants, and socks of the same color?

Answer 1

0.20 or 20%

Explanation:

Brown shoes = 3

Black shoes = 2

Total shoes = 5

Brown pants = 1

Black shoes = 3

Total pants = 4

Brown socks =4

Black socks = 6

Red socks = 2

Total socks = 12

In order to choose shoes, pants and socks of the same color, Teddy can go either all black or all brown. For all black, there is a 2 in 5 chance he gets the right shoes, 3 in 4 chance for pants and 6 in 12 for socks. For all brown, there is a 3 in 5 chance he gets the right shoes, 1 in 4 chance for pants and 4 in 12 for socks.

`P=P(All\ black)+P(All\ brown)\\P=(2)/(5)*(3)/(4)*(6)/(12)+ (3)/(5)*(1)/(4)*(4)/(12)\\P=0.20`

The probability that he chooses shoes, pants, and socks of the same color is 0.20 or 20%.