In which the author explicates some elementary probability theory to show that why universal testing for COVID-19 is a silly idea
As an aid to another discussion elsewhere regarding the latest pandemic, consider the effect of screening for the Dreaded Red Squamish of which, unbeknownst even to Health Care Professionals, infects 5% of the population.
The test, which includes the person administering it, the instruments, conditions, and all what have you, is known to be 95% sensitive -- of those with the Squamish, the test will come back positive 95% of the time -- and 95% specific -- of those without the Squamish, the test will come back negative 95% of the time.
Perceptive Reader will notice that this means a 5% risk of a false positive and a 5% risk of a false negative. The Usual Suspects may cry, "No fair!" because they want Daddy and Mommy to ensure 100% perfect. [When do we want it? Now!] But the sensitivity is about normal for lab tests while the specificity is actually better than normal. (As an example of lack of specificity is the well-known ability of drug testing to detect the consumption of poppy seed bagels.) It is also hard to imagine that the 15,000th test will be performed with the same sprightly verve and enthusiasm as the 1st.
Now, test a million people for the Red Squamish, just in case.
Of course, 5% false positive or negative is way exaggerated - it's more like 20 - 30 % for each in most clinical tests. Yesterday I posted a comment where the authors discovered 50% false-positive