Bayes' theorem
Bayes’ theorem is a rule in probability theory that relates the conditional probabilities of two events. It provides a basis for updating an existing probability when new evidence becomes available.
If a disaster has a 0.1% chance and a 99%-accurate alarm is installed, out of ~110 alarm days in 10,000, about 100 are false alarms. Over 90% are wrong—yet dismissing the alarm means ignoring a 99%-accurate warning. This is the "base rate fallacy," where probability defies intuition.
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