CV and mad panic behaviour

[Mav]

The accuracy of tests has to be considered alongside how rare (or otherwise) an illness is.

A common problem in probability classes is as follows:

A test for a certain rare disease is assumed to be correct 95% of the time: if a person has the disease, the test result is +ve with a probability of 0.95  & if the person doesn't have the disease the test result is negative with probability 0.95. A person drawn at random from a certain population has a 0.1% chance of having the disease.

Q. What's the probability that a random person who tests positive actually has the disease?

Due to the vagaries of conditional probability, the answer is surprisingly 0.01866 (1.866%). You'd think a test that's 95% would translate to a 95% chance of a correct positive, wouldn't you?

Of course, the chance of a random person having Covid is higher than 0.1% given that around 0.1% of the Victorian population are reported as new daily cases.