Math CentralQuandaries & Queries


Question from Peter, a student:
Rick has 6 different pairs of socks. Whats the probability that two randomly selected socks will be from a matching pair?

Hi Peter,

There are two ways of approaching this question:

1. The two socks are pulled simultaneously from the drawer.

As there are 12 socks in total, and we are taking 2 of them, there would be 12C2 = 66 ways to do this.
Of these 66 2-sock combinations, 6 of them would correspond to the matched pairs of socks.

Therefore the probability of getting a matched pair would be 6/66 or 1/11 ( 0.090909...)

2. One sock is pulled and then a second sock is pulled.

The probability of the second sock matching the first sock pulled can be found by the simple probability formula:

# of successful outcomes =
since there is only one sock that will match left in the drawer
# of possible outcomes
since there are 11 socks left in the drawer

As you can see, regardless of how we approach this problem, we get the same probability.

Hope this helps,

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