Predict first: Prevalence is 0.1%. A test detects every infection, but 1% of healthy people test positive. After one positive result, is the probability of infection closer to 9%, 50%, or 99%?
Imagine 100,000 people
True positives—
False positives—
P(condition | +)—
After + on Test 1 and Test 2—
What changes after a second, conditionally independent test?
Why not simply run the same test twice?
Multiplying the two likelihoods assumes the test outcomes are conditionally independent given disease status. Repeating the same measurement may violate that assumption because the errors can be correlated.
The lecture’s follow-up-test calculation works by assuming Test 1 and Test 2 are conditionally independent given the true state.