Question

Canton does not like to pair his socks, so he throws them all in a drawer. He has three pairs of brown socks, three pairs of navy socks, and four pairs of black socks. On a dark morning, he pulls out two socks. What is the probability that he pulls out a black pair?

Answer 1

The probability that Canton pulls out a black pair of socks from the drawer is 2/15.

Step-by-step explanation:

To find the probability that Canton pulls out a black pair of socks, we need to determine the total number of pairs of socks in the drawer and the number of black pairs of socks.

There are three pairs of brown socks, three pairs of navy socks, and four pairs of black socks. So, the total number of pairs of socks in the drawer is 3+3+4 = 10.

When Canton pulls out the first sock, there are still four pairs of black socks in the drawer. So, the probability of pulling out a black sock on the first try is 4/10.

After the first sock is pulled out, there are three pairs of black socks remaining in the drawer. So, the probability of pulling out a black sock on the second try is 3/9.

To find the probability of pulling out a black pair, we need to multiply the probabilities of pulling out a black sock on the first and second try. Therefore, the probability of pulling out a black pair of socks is (4/10) * (3/9) = 12/90 = 2/15.