The false positive rate has nothing to do with positive examples (hugely counterintuitively). A false positive happens when there's nothing there but you think there is. The rate of these is compared to all incidents where there's nothing there. So it's the fraction of negative instances where you think there's a positive. No actual positives have to come into the picture.

Ah you're right that makes a lot of sense thanks for the explanation

Suppose you test for 1 true positive out of 1001 cases.

You are likely to find the actual positive and 50 false ones.

However, that’s with a single test. If you run 5+ different tests you are likely able to distinguish the true positive.

To add to this, you can't just run 5+ tests. You have to run wholly independent ones.