I'm happy to see a real

"statistician". You are right. Actually, I intended to give the conditions clearly like this:

P(HIV+|infection) = 0.95; P(HIV-|infection) = 0.05;
P(HIV+|non-infection) = 0.05; P(HIV-|non_infection) = 0.95;

But, I just felt it troublesome and may scare somebody away. HaHa.