But, that's the thing about randomness. Sure, you might get an even distribution, but, there's no guarantee of that. It's equally possible that you get group in random choices, meaning that you might wind up wiping out everyone with any medical training, for example, simply through random chance.
Technically, that could happen, yes, but it is not "equally possible".
The best way to see this is probably with a much smaller example. Imagine a room with 10 people in it when Thanos snaps his fingers. Five of these people are doctors, the rest are not. What is the chance that you lose the five doctors, and none of the others in the room?
The number of different groups of five that might be chosen is given to us by combinatorics - and if I hae my numbers right, there are 252 distinct groups of five you could choose. Only *one* of these is all the doctors. So, the chance that you lose all the doctors is 1 in 252, or just under 0.4%. Not likely.
It is as likely as any other *particular* arrangements (like, say, 4 of the doctors and Fred). But we are implicitly comparing "lost all the doctors" to "not lose all the doctors" - teh ensemble of possibilities where all teh doctors are dead is small compared to *all the other * possibilities, which include some living doctors.
Or, to put it more graphically - There are something over one million doctors in the US. The chance of losing all the doctors is basically the same as the chance of losing specifically the entiretyof Dallas, Texas (which something over 1 million people). When Thanos snaps his fingers, do you expect to then walk into Dalls, specifically, and find it completely and utterly empty? No. That's not a likely scenario. Same thing here.