## Quick Reference

Title used for the ‘law of large numbers’ in probability theory, proved by Jakob Bernoulli (1654–1705). The theorem provides the best-known link between probability and the frequency of occurrence of events in a sequence of trials. It is thus fundamental to the epistemology of probability. Bernoulli showed that if we have a sequence of *n* trials, on each of which an outcome has probability *p*, then the most probable number of times the event occurs is *pn* (or the nearest integer to this); furthermore for any small number e, the probability that the frequency of occurrence falls within the interval *np*±*e* increases with *n*, and approaches 1 as n approaches infinity.

*Subjects:*
Philosophy — Mathematics.