The key is not to find "who gets HIV" vs. "who does not get HIV." Instead, we are trying to measure "who gets exposed" vs. "who gets HIV." Although we do not kn

The key is not to find "who gets HIV" vs. "who does not get HIV." Instead, we are trying to measure "who gets exposed" vs. "who gets HIV." Although we do not know how many people are exposed in each group, we can make sure that the number of exposed people in each group is approximately the same by increasing the number of people vaccinated. If we know that the same number of people are exposed (which is less than the sample size), then the number of people who get sick is much more significant. By increasing the number of vaccinated people, the number of exposed people becomes more equal between the two groups since a few "more exposed/risky people were assigned to group A" will have a less significant impact.