The Laws of Coincidence

Abstract

Anomalous events often lie at the roots of discoveries in science and of actions in other domains. Familiar examples are the discovery of pulsars, the identification of the initial signs of an epidemic, and the detection of faults and fraud. In general, they are events which are seen as so unexpected or improbable that one is led to suspect there must be some underlying cause. However, to determine whether such events are genuinely improbable, one needs to evaluate their probability under normal conditions. It is all too easy to underestimate such probabilities. Using the device of a number of ‘laws’, this paper describes how apparent coincidences should be expected to happen by chance alone.