4. Base rate fallacy. The correct answer is (e), or 0.98 percent. The base rate fallacy occurs when you don’t notice that the failure rate (1 in 100) is the not the same as the false alarm rate. The false alarm rate is completely different, because there are, after all, far more nonterrorists than terrorists. Let’s imagine that we walk everyone—100 terrorists and 1,000,000 nonterrorists, for a total of 1,000,100 people—in front of the face recognition tool. A 1 percent failure rate means it’s going to ring incorrectly one time for each 100 passengers, 10,099 times in total. It will catch 99 terrorists and miss 1, but it’s also going to catch 10,000 nonterrorists.

The ratio is actually 99/10,099, or a miniscule 0.98 percent, that the person caught is actually a terrorist.