Problem #WSP-000405

Problem

Imagine there’s a disease called ‘mathematitis’ which $1\mathrm{\%}$ of people have. Doctors create a new test to discover whether people have mathematitis. The doctors fine-tune the test until it’s $99\mathrm{\%}$ accurate - that is, if a person $A$ has it, then $99\mathrm{\%}$ of the time the test will say that $A$ has it, and $1\mathrm{\%}$ of the time the test will say that $A$ doesn’t have mathematitis.

Additionally, for person $B$ who doesn’t have the disease, $99\mathrm{\%}$ of the time the test will correctly identify that $B$ doesn’t have it - and the other $1\mathrm{\%}$ of the time, the test will say that $B$ 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?