What are the odds that my daughter's socks drawer contains exclusively single socks? Over 20 socks but not a single pair

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?).
- I knew I was at the right place.
- This seems so unlikely that it may be done on purpose. Is there a way to calculate the probability of this being on purpose? For instance, if she had 30 pairs of socks to start with, it seems unlikely to reach 20 single socks if they are randomly lost. Intuitively it should depend on how far we are from the expected value of single socks after losing N socks, but idk how to model nor calculate this.

This sort of thing is why I try to get a homogenous collection of socks.
- I almost only wear wool socks, the ones with the red line at the top. Been doing so for a loooong time lol.
  
  Like the kind every sock monkey is made from?
- This is why I have matching 10 pairs of summer socks, and matching 10 pairs of winter socks.

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

Next age range, buy like 20 pairs of identical socks.
- That's what I do for myself. Works great.
- And lose 39 of them??
- Y'know I tried that once, and the build quality didn't turn out great, so I was left with 20 pairs of crappy socks.

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

washing machine deduplication glitch, add it to the ticket
- There's an old TV show in Quebec, a space crew looking for new planet for humanity. In one episode they stubble accros a space field of lost socks, and discover there's a some sort of black hole in washing machines that sucks in socks.

Pretty high if she did that on purpose
- Nah, she's too young for to be playing a trick on me. Whenever she gets home, the fist things she does is taking off her socks, so we find socks everywhere in the house. She often wears mismatched socks, but this just baffles me. Not a single pair, I swear that's the content of the drawer.
  
  Whenever she gets home, the fist things she does is taking off her socks,
  Watch her take off the socks noting where she leaves each one. Could we be seeing a higher rate of lost socks because of how she chooses to discard the left sock from her foot vs the right sock? Is there perhaps a piece of furniture underneath which is all the missing mates to her socks?

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.

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.

Some people like wearing mis-matched socks and do so on purpose. Maybe she's one of those people?
- Yep, she just randomly takes any socks from the drawer. It's not a fashion statement, just lazyness lol.

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.
- That's why I uniformly sample my socks.

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.