Sorry,
using that reasoning, in the origin each of the 2s would have a 10% chance of being drawn, and the 12 would have a 60% chance of being drawn.
Once the 20 are added to one of the 2s then there are 22 of that color in the box (obviously). This means that the remaining 2s have a 5% chance of being drawn, the 12 now have a 30% chance of being drawn, and the 22 have a 55% chance of being drawn.
It's not even close. Not by a long shot.