It's therefore worth remembering when inverse probabilities

*are*equal to one another, so as to take inferential precautions when they are not. A simple implication of Bayes' theorem is that the conditional probability of A given B is similar to the conditional probability of B given A when the probabilities of A and B are close to one another. If there were approximately the same number of terrorists as there were people behaving suspiciously, and most terrorists behaved suspiciously, then one could infer that most suspiciously-behaving people were terrorists.

The opposite is also true. If there is a big discrepancy between the probabilities of A and B, the conditional probabilities will also differ significantly, the exception being when there is zero probability that A and B can be true together.

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