But you don't know that your partner has AIDS, so you have to take that probability into account too. But the probability of condom failure and finding an AIDS infected partner are independent events - the sample spaces are not affected by each other, as far as I can see. So if you choose a partner at random, and the odds that that person will be AIDS infected are .20, then the odds of condom failure and getting an AIDS infected partner for a single sex act is .03*.20, or .006, or six chances in a thousand that A and B will occur, and 994 chances in a thousand that one or both of those events (condom failure or having an AIDS infected parter) will not happen.
But since we're assuming that you only have to lose once to get AIDS, you need to figure up the probability that both of those events will eventually happen given some number of sex acts. Assume you choose a new partner at random every week, for 52 weeks of the year. Then the probability that both events (condom failure and getting an AIDS infected partner) will not occur across the span of a year is .994^52, or about .731. Across ten years, the probability of both events not occurring simultaneously - because you need both events to happen simultaneously to get AIDS - is .994^520, or about .04 - that is, there's about a 96% chance that both of those events will occur simultaneously over the span of ten years.