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 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 = 1 since there is only one sock that will match left in the drawer # of possible outcomes 11 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,
Leeanne

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