The spam filter

Question

In a batch of 10,000 emails, 10 are genuine phishing attempts and the filter flags all 10. The filter also flags 90 of the safe emails by mistake. You find an email sitting in the flagged folder.

What is the probability that it is really phishing?

Accepted Answer

Count the two kinds of flagged emails. - Real phishing that got flagged: 10. - Safe emails wrongly flagged: 90. Total in the flagged folder: 10 + 90 = 100, of which only 10 are truly phishing. So P(	ext{phishing} \mid 	ext{flagged}) = \frac{10}{100} = \frac{1}{10} = 10\%. The filter never misses a phishing email, yet a flagged message is genuine only one time in ten, because safe emails vastly outnumber phishing and even a small error rate on them fills the folder with false alarms. Takeaway. With a rare target and a large clean population, a flag mostly signals a false positive. A "catches…

The spam filter

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