The base rate fallacy

Amongst my favorite fallacies lies the base rate fallacy.

Here’s a great introduction to this fallacy on the BBC’s website.

Imagine you’ve invented a machine to detect terrorists. It’s good, about 90% accurate. You sit back with pride and think of the terrorists trembling.

You’re in the Houses of Parliament demonstrating the device to MPs when you receive urgent information from MI5 that a potential attacker is in the building. Security teams seal every exit and all 3,000 people inside are rounded up to be tested.

The first 30 pass. Then, dramatically, a man in a mac fails. Police pounce, guns point.

How sure are you that this person is a terrorist?
A. 90%
B. 10%
C. 0.3%