Sock probability
© 2 September 2021 Luther Tychonievich
Licensed under Creative Commons: CC BY-NC-SA 3.0
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When I pull two socks from a pile, they usually match.


I wear black socks with separated toes and turned heels. Because the inner toe is larger than the outer toe and there’s a heel, left and right socks are distinct.

When I launder my socks, I sometimes pair them all up but other times I simply put them in a pile. Taking them from the pile, it seems like more often than not the first two socks I grab are a matched pair. Could that be?

Rather than keeping tally to correct my instinct, I decides to do a bit of math:

The more socks I have, the closer to 50/50 it gets, but I’m always more likely to get a matching pair than not. As a pull socks from a pile of ten pairs, removing them from the pile, I expect to get a matched pair on the first try just over six of the ten times I put on a pair of socks.

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