The Busy Hospital

Scenario

A hospital tests all incoming patients for a rare condition that affects 1 in 1,000 people. The test is 99% accurate — it correctly identifies positive cases 99% of the time, and correctly rules out negatives 99% of the time. A patient just tested positive.

Question

What is the approximate probability the patient actually has the condition?

1. A.99% — the test is 99% accurate
2. B.About 50% — it could go either way
3. C.About 9% — most positives are false alarms
4. D.About 0.1% — the condition is too rare to matter