Owen has your answer for you here but something I noticed was a part of your math that could tell you the idea was wrong before you checked the final percentage: When you were adding the percentages, you ended up with .895 or 89.5% chance of getting a positive result from the test (you added all the positive odds, with the thinking that they're independent and referring to the same group). But it's fairly clear that more than 10.1% will get negative results, so the addition of those probabilities can't be right (This is more useful to way to check if you know the negative rate but not the quantity amount).