Definition
Frequentist probability defines the probability of an event as the limit of its relative frequency over a large number of independent repetitions of the underlying experiment. If a thumbtack lands point-up in 37% of 10,000 throws, the frequentist says its probability of landing point-up is approximately 0.37.
The interpretation is rooted in the law of large numbers, which guarantees that observed frequencies converge to the true probability as the number of trials grows. It dominates classical statistics and underlies most of the inference techniques taught in introductory courses — hypothesis tests, confidence intervals, p-values.
Why it matters
How it works
A frequentist analyst designs an experiment so it could in principle be repeated, then collects data and computes frequencies. To test a hypothesis, they ask: 'If the hypothesis were true, how often would I see data this extreme by chance?' That question is the p-value, and it is meaningful only because of an imagined long run of repeated experiments.
The interpretation is operational and externally checkable, which is part of why it became the dominant approach in the 20th century. It is, however, criticised for awkwardly handling beliefs, prior information, and unique events — the gaps Bayesian probability tries to fill.