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It isn't a 3% chance of a false negative, the 97% figure is conditioned on actually having HIV. The actual chance of a false negative is far lower, since most people don't have HIV at all.

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Good point. You could also realistically eliminate those who know they are infected from the potential false-negative category, which would give you an initial pool of 240,000[1] potential infected who don't know they're infected. Among them there is a 3% chance of non-response within 3 months to antibody testing, for a total of 7,200 false-negative potential candidates out there among 309,000,000 total Americans. Then consider the 1 in 20,000 odds [2] of being a match, and you end up with a false-negative match rate of 0.00117 per million people (according to wolfram alpha [3]).

I probably screwed something up, but in any case you are definitely right that the false-negative odds are very low among all potential applicants. Really makes the argument against seem foolish.

1) http://www.cbsnews.com/8301-504763_162-57333212-10391704/cdc...

2) http://www.organtransplants.org/understanding/marrow/

3) http://www.wolframalpha.com/input/?i=%28%281%2F20000%29++*+%...

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