socks which may or may not match

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.

There are two situations that matter when picking the last sock:

1) we have one extra of one sock.
- this is the situation mentioned by deusovi. 50% either way.

2) we have three extra of one sock.
- 50% we get the extra sock and we throw out the situation.
- 50% we get the lesser sock and we increase the probability of having one unmatched set.

Therefore we are more likely to have one unmatched set.

I believe that

EDIT:
**In the question, the statment: "with a 50/50 probability" could be related to EACH DRAW as opposed to a cumulative effect. I chose the cumulative approach:

The probability is that the color of the second-to-last sock chosen is unlikely to be chosen last. There are, in this scenario, more likely to be more of the other sock color available in the pool, so choosing two of the "second-to-last" color twice in a row is less likely than choosing one that is (in all reasonable probability) in greater supply. The socks are more likely to be paired. Doesn't matter if there are 2016 socks, 2,106,000 socks or just two socks. The probability is the same. The second sock is probably a different color.