> You go to the doctor and get a test. Nitpick here. There's nothing wrong with the math of Bayesian probability, but the setup is usually something like an ST

> You go to the doctor and get a test. Nitpick here. There's nothing wrong with the math of Bayesian probability, but the setup is usually something like an STD test, and in those cases the prior is wrong. Our prior probability shouldn't be "0.01% (1 in 10,000) of the population is infected," we really want % of infection for the population that get tested. This is really obvious with disease tests because people don't typically get tests without reasons (symptoms, contact with infected persons, etc.). The math as-is would only work if we're sampling people randomly.