Ha! nice. (Although in my defense, I did say "roughly".) What is interesting about this problem is (1) you can have more confidence in a negative result being accurate [iF, that is, your original premise of 10% 'real' infections is correct, which itself is based in part on the assumption of accuracy of testing!], and (2) it's not strictly a probability problem, since you cannot know WHY you are getting a false positive, and the existence of false positive may not be purely random. If it were random, then re-testing would solve things. But apparently, no one is willing to assume that. It's nice that we are now applying these models to the efficacy of vaccination rather than testing!