I think you may be close but likely for the wrong reasons. I had to sit down with this for a moment to feel comfortable with it. If we take your 10% base rate

I think you may be close but likely for the wrong reasons. I had to sit down with this for a moment to feel comfortable with it. If we take your 10% base rate to be disease prevalence, that gives us 100 sick and 900 well. Of the 100 sick, something with 90% sensitivity should get me 90 true positive tests and 10 false negative tests. Of the 900 well, I should expect to see for a test with 90% specificity, what, 80 false positives and 810 true negatives? if I did my arithmetic right?