Suppose that you are worried that you might have a rare disease.

You decide to get tested; the testing methods for this disease are correct 99% of the time (in other words, if you have the disease, it shows that you do with 0.99 probability, and if you don’t have the disease, it shows that you do not with 0.99 probability). Suppose this disease is rare, occurring randomly in the general population in 1 of every 10,000 people. If your test results come back positive, what are your chances that you actually have the disease?