It’s 1 in 5. Six possible pairings can be drawn from the hat:

red 1 / red 2
red 1 / white
red 2 / white
red 1 / blue
red 2 / blue
white / blue

We know that the last has not been drawn. That leaves 5 possible combinations, so the possibility of red 1 / red 2 is 1 in 5.

“Many people cannot accept that the solution is not 1 in 3,” writes Erwin Brecher, “and of course it would be, if the balls had been drawn out separately and the color of the first ball announced as red before the second had been drawn out. However, as both balls had been drawn together, and then the color of one of the balls announced, then the above solution, 1 in 5, must be the correct one.”