Problem #WSP-000407

Problem

Some doctors make a new test for the disease ‘mathematitis’ which is even better. This new test is $99.9\mathrm{\%}$ accurate - meaning that $99.9\mathrm{\%}$ of the time when someone has the disease, the test will say so. And when someone doesn’t have the disease, $99.9\mathrm{\%}$ of the time the test will say that they don’t have it.

Paul goes to the doctor and test positive for mathematitis. What’s the chance he actually has mathematitis? Recall that $1\mathrm{\%}$ of the population has mathematitis.