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However, to sum it up, if the probability of getting AIDS is 0.006 then that's what it is each time you have intercourse.

Right - that's the odds for a single occurence. But he wants to know the cumulative odds for multiple sex acts over some period of time, so you have to take that probability and raise it to the power of the number of discrete acts in order to calculate those odds. IOW, the odds that you will not flip heads on any given coin toss are 50%. The odds that you will not flip any heads across ten coin tosses are pretty small - about 1 in 1000.

I don't think we disagree. Since the probability of heads is .50 for any fair toss, assuming a perfectly fair coin, over a random number of tosses (greater than, say, 100), you would expect 50% of the tosses to be heads and 50% to be tails. You are interested in how likely it is that at least 1 out the sample universe will be tails (condom failure). That probablity would, as you say, approach unity.

However, it seems to me that this problem is not amenable to sound statistical analysis on the facts given. The second probalistic variable, the HIV infection rate at 20%, does not adequately capture the decision tree facing individuals: after all, who sleeps randomly with 500 different partners over 10 years from a population which mirrors the overall probablity of having aids. All of us move in circles that can best be characterized as subpopulations at greater or lesser risk of aids: i.e. the monogomous spouse who only has relations with his or her spouse to whom he or she has been married since before 1980 faces a very different risk probability (assuming exactly the same facts about condom use and failure rates) than does the promiscuous homosexual who frequents the bath houses for a bit of rough anal trade every week.

While statistic analyssi can be highly enlightening in many circumstances, you can't do meaningful work when you can't control for the variables in an analytically usefeul way.