This seems very weird. Where does this come from? I'd assume none will guess correctly because you have countably infinite guesses from uncountably infinite se

This seems very weird. Where does this come from? I'd assume none will guess correctly because you have countably infinite guesses from uncountably infinite set (the colors) so the set of guesses is very sparse, meaning pretty much none will hit it. How on earth can almost all hit a point in a continuum exactly with random chance?