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| Math Central | Quandaries & Queries |
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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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