Rare Disease Flip

A disease affects 1% of a population. A test has a 95% true positive rate and a 10% false positive rate. Given a random person tests positive, which expression gives P(disease | positive) via Bayes rule?

A

0.95 * 0.01

B

0.95 / (0.95 + 0.10)

C

(0.95 * 0.01) / (0.95 * 0.01 + 0.10 * 0.99)

D

(0.95 * 0.01) / (0.10 * 0.99)

E

(0.10 * 0.99) / (0.95 * 0.01 + 0.10 * 0.99)