Question

Without looking Jenny randomly selects two socks from a drawer containing four blue, three white, and five black socks, none of which are paired up. what is the probability that she chooses two socks of the same color?

Answer 1

`19/66`

Explanation:

We can add the probability of choosing two blue, two white or two black socks, since they are mutually exclusive possible outcomes.

The total number of socks is `4+3+5=12`

The probability of choosing two blue socks is:

`4/12*3/11 = 1/11`

The probability of choosing two white socks is:

`3/12*2/11 = 1/22`

The probability of choosing two black socks is:

`5/12*4/11 = 5/33`

In each case, the probability that the first sock is a particular colour is the number of socks of that colour divided by the total number (`12`) of socks. Once one sock of that colour has been removed, the probability of the second sock being the same colour is the number of socks remaining of that colour divided by the remaining total (`11`) number of socks in the drawer.

So the probability of choosing any pair with matching colour is:

`1/11+1/22+5/33 = 6/66+3/66+10/66 = 19/66`