The airport threat scanner

Question

An airport scanner flags 99% of the (very rare) real threats and 1% of innocent travelers. Suppose that 1 in 1,000,000 travelers is a real threat.

Of everyone the scanner flags, roughly what fraction are real threats?

Accepted Answer

Run one million travelers through the scanner. - Real threats: 1 person, flagged with probability 0.99, so about 1 flag. - Innocent travelers: the other 999,999, of whom 1% are flagged, giving about 10{,}000 flags. Total flags: roughly 10{,}001, of which about 1 is a real threat. So P(	ext{threat} \mid 	ext{flagged}) \approx \frac{1}{10{,}001} \approx 0.01\%. Almost everyone the scanner stops is innocent. When the thing you are hunting for is one in a million, even a 1% false-alarm rate on the enormous innocent population buries the single real case under thousands of false positives. Takea…

The airport threat scanner

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