Practice question · Multiple choice
A test for a disease affecting 1 in 1000 people is 99% accurate. You test positive. Why is the chance you have it closer to 9% than to 99%?
Hints
- Take 1000 people. How many are sick? How many healthy people does a 1% false positive rate flag?
- Count the positives and ask what fraction of them are genuinely ill.
Show the answer
B. Because false positives from 999 healthy people outnumber the 1 true one
Why
In 1000 people: one true positive, and about ten false ones from the 999 healthy. So roughly one positive in eleven is real. Base rates dominate when a condition is rare, the reason screening programmes for rare diseases generate so much needless alarm, and the commonest failure of medical intuition.
Practise Conditional Probability and Independence
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