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

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.