Then we go negative and we go through zero again, which correlates to the second area of zero, that shows up also in our probability density plot, and then we're positive again 0 and approach zero as we go to infinity for r.
If one in 1, 000 people have a disease and the false-positive rate for a test is 5%, then the probability that a person testing positive has the disease is at most 2%.
The probability of a false positive in a chemical assay for a drug or poison (something appearing to show up when it isn't really there) is reasonably well known.