False positive and false negative rates are important to bear in mind in a mass testing scenario.
By way of example: you reside in an area with a 1 in 1,000 background probability of infection with blanket testing. You take a test, get a positive result. You learn the test has a 1% false positives, and 10% false negatives. What is the probability you are infected?
Let’s assume are infected from tests, which accords with the probability.
are not infected.
Probability is then true positives over all positive test results
If we then re-test all the positives we can take as our background probability, which means that a second positive test result will yield a much higher probability of infection.