The False Positive Paradox

A disease affects 1 in 100 people. A test for it has:

• 99% sensitivity — if you have the disease, it catches it 99% of the time.
• 90% specificity — if you don't have it, the test correctly says so 90% of the time (10% false positive rate).

You take the test. It comes back positive. What's the probability you actually have the disease?