You just won 2016 socks. Some of them are white, some are blue. The color of each sock was randomly chosen, with a 50/50 probability. Is it more probable that the socks can be paired, or that you will remain with two unmatching socks?
Answer
The probability of "pairability" is...
exactly 50%.
Consider what happens when all but one of the socks has been chosen. You'll have one color that has an even number of socks, and one that has an odd number. The last sock is equally likely to be either color: if it's the even color, then you'll have leftovers, and if it's the odd color, you'll be able to match every sock up.
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