Currently it is estimated that 3 out of every 1000 Californians are infected with
coronavirus. The so-called rapid "antigen" test for coronavirus has a very low false
positive rate of just 0.05, but has a high false negative rate of 0.2. The so-called
PCR test is more reliable: it has an even lower false positive rate than the antigen
test, namely only 0.001, but even more importantly its false negative rate is much
lower at 0.01.
What is the probability that you have a coronavirus infection conditional on your
PCR test has coming back positive?