False Positives and Base Rates

Level 2●●●○○ Medium~5 min

Problem

A disease affects 11 in 10001000 people. A test has 99%99\% sensitivity (true positive rate) and 95%95\% specificity (true negative rate). You test positive. What is the probability you actually have the disease? Most people guess around 99%99\% — why are they so wrong?