Standard screen for research and data roles.
The test that is usually wrong
The question
A condition affects one person in a thousand. A test detects it 99 percent of the time and has a 5 percent false positive rate. You test positive. What is the probability you have it?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
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The answer
About 2 percent.
Take 100,000 people. About 100 have the condition, and 99 of them test positive.
The other 99,900 do not, and 5 percent of them, around 4,995, also test positive.
So roughly 5,094 positives, of whom 99 are genuine: about 1.9 percent.
Working in counts rather than probabilities is faster and far less error prone out loud. The general lesson is that a rare event plus an imperfect test is dominated by false positives.
What it is testing
Base rates, which almost everyone underweights when the test sounds accurate.
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