Suppose that the prevalence of breast cancer in the population of women is 1 percent. Suppose that the sensitivity of a breast cancer test (its true-positive rate) is 90 percent. Suppose that its false-positive rate is 9 percent. A woman tests positive. What is the chance that she has the disease? The most popular answer from a sample of doctors given these numbers ranged from 80 to 90 percent.3 Bayes’s rule allows you to calculate the correct answer: 9 percent.
