[general_re]

The good doctor is much more of an expert than I, so perhaps a ping for help is in order.

That being said, my initial reaction is that condom failure and having an infected partner are independent events - it's not a conditional probability at all, and therefore your simple probability calculation is correct. And even if it was a matter of conditional probability, your opponent muffed his own math - he gives the conditional probability P(A|B) as being (P|A)*(P|B)/(P|B), but it's not. The actual formula is P(A|B) = P(A)*P(B|A)/P(B). The Mathworld page on conditional probability shows how that's derived.

[Doctor Stochastic]

The original math is correct under the stated assumptions.

First that condom failure is "random" in that one doesn't get a bad batch of condoms or a good batch.

Second, that the partners are chosen "randomly" (independently and identically distributed); a succession of one-night stands would be an example. Things would be different with a single partner who was known to be HIV positive.

The math is correct. The actual probabilities would have to be obtained through observation.

I didn't really understand the objection; it seemed to be poorly written.