Two positive tests
A disease has 1% prevalence. A test has 95% sensitivity and 90% specificity, and repeated runs are independent given the true status. A patient tests positive on two independent runs. What is the probability the patient has the disease? Give your answer as a decimal (to 2 decimals).
Show hints (2)+
- Two independent positives multiply the likelihoods: for diseased, for healthy.
- Equivalently, use the single-test posterior as the prior for the second test.
Answer
Reveal answer →Final answer
0.48 (± 0.01)
Create a free account to see the full worked solution and track your progress.
Interview format: Hedge Fund Quant, Systematic & Data-Driven Trading