This turns out to be a more difficult (and somewhat deceptive) problem than I first thought.
The answer is that 75% of the balls are red. This is because the only viable solution seems to be when there are a total of 4 balls, and 3 of them are red. (You cannot get the same results with 8 balls 6 of which are red, etc)
TomM has submitted a fairly rigorous proof to this in the problem's comments.