Problem
Imagine there’s a disease called ‘mathematitis’ which of people have. Doctors create a new
test to discover whether people have mathematitis. The doctors fine-tune
the test until it’s accurate -
that is, if a person has it, then
of the time the test will say
that has it, and of the time the test will say that
doesn’t have mathematitis.
Additionally, for person who
doesn’t have the disease, of
the time the test will correctly identify that doesn’t have it - and the other of the time, the test will say that
does have
mathematitis.
Suppose you don’t know whether you have mathematitis, so you go to
the doctors to take this test, and the test says you’ve got it! What’s
the probability that you do actually have the disease?