[wtallis]

That link says the Bertrand paradox only applies when the domain of possibilities is infinite. That doesn't seem to cover tasks like randomly selecting people from a finite population.

[PlatoIsADisease]

Its not number of people, but number of ways to slice the situation.

In this case: Do we use IQ tests? Do we use random numbers and allow babies to win?

If you want to be traumatized about statistics, I like this video: https://www.youtube.com/watch?v=xy6xXEhbGa0