Puzzle

There are a certain number of blue balls and a certain number of red balls in an urn. You pick up two balls from the urn randomly. If you find that they are opposite in colours, you throw them and put a red ball in the urn. If they are of the same colour, you throw them and put a blue ball in the urn.

Thus you are reducing the number of balls in the urn one at a time no matter what the case is. After going through it again and again. Only one ball will be remaining in the end. If you are told the respective number of blue and red balls at the outset, will you be able to predict the colour of the final ball?