Off the top of my head, if we formulate it as: what are the chances that out of 10 pairs of socks we randomly pick 1 of each so that we end up with 10 non-matching socks, that is calculable and certainly the chances would be extremely low, but I can’t be bothered to calculate it precisely. Also, it’s easy to get these things wrong. I’d think that if there’s N socks in total it would be something in the order of 1/N! So yeah pretty low odds indeed.

100% if she's throwing them away as a style choice

Technically, she could have lost way more, she just successfully lost both.

But if she starts with 20 pairs, and only loses a sock if she wears it, and only wears matching pairs, and only wears one pair per day, and has ~5% chance of losing exactly one sock on any given wear, then you'd expect her to lose a sock every 20 days, so after ~400 days she would have lost one from every pair.

I guess the real question is how long did it take to reach this point, so we can calculate the odds of her losing a sock on any given day (there's a "sock market" pun in here somewhere, I'm sure....sonks?).

Matching socks is overrated. They’re almost all pink so let her get creative with pairing them. :)

This sort of thing is why I try to get a homogenous collection of socks.

washing machine deduplication glitch, add it to the ticket

Next age range, buy like 20 pairs of identical socks.

Depends on how many pairs the drawer started with.

I'm imagining that initially there were say 100 socks in the drawer (50 distinct pairs) and each day she randomly chooses two socks (already very unlikely to be a pair) and has some chance of losing one or both.

In this scenario it does seem intuitively reasonable that when it gets down to 20 there might not be any pairs left, but I don't know how to math it. I am pretty sure that the higher the number of initial (non-overlapping) pairs, the more likely it will end (at 20) with none left, but again the math is beyond me.

I work in child care. If you don't glue something important to your child, they'll lose whatever it is. Our school's lost and found looks like a thrift store was set up in the middle of the school. Honestly it's astounding. If I came home without my jacket, being cold would be the lest of my issues.

Maybe she threw out the worse-looking token of each type in an attempt at housekeeping

That's not really something you can calculate the odds on, because the socks in the drawer weren't chosen from a larger set

Unless you assume that each one had a mate, and you want to know the odds that, when starting from 20 socks, when she picked two socks each day for 10 days she picked half of two pairs. I'm not sure how you calculate those odds, but it'd be very unlikely.

50/50?

Pretty high if she did that on purpose

Some people like wearing mis-matched socks and do so on purpose. Maybe she's one of those people?