Statistics problem

I have a statistics problem that I just can not figure out the answer to: What is the probability that a namefag is neither a troll nor a moron? I think the answer is 0, but I haven't been able to prove it yet.

fixed
1.namefag probability of being moron=x/100
2.namefag probability of being troll=y/100
3.namefag probability of being moron or troll=(x+y)/100- (x/100*y/100)
4.namefag probability of being moron and troll=(x/100*y/100) *
5.namefag probability of being neither moron/troll=(100-(x+y)/100- (x/100*y/100))/100
6.*If the distribution is uniform(unbiased).