Your mistake is here: > The possible values of N are evenly distributed [1...100] (we discount the N=0 case because we drew a red ball) These probabilities ov

Your mistake is here: > The possible values of N are evenly distributed [1...100] (we discount the N=0 case because we drew a red ball) These probabilities over N are not actually even anymore; the fact that you drew a red ball means that higher values of N are more likely.