Two Schools of Thought

Frequentists define probability as the long-run frequency of an event — flip a coin a million times and heads appears about half the time. Bayesians treat probability as a degree of belief, updated as evidence accumulates. Both frameworks are mathematically valid, but they lead to surprisingly different conclusions in ambiguous situations.

Neither school is wrong — they answer different questions. A frequentist asks how often something happens in repeated trials. A Bayesian asks how confident you should be given what you know right now. In practice, modern statistics uses both frameworks depending on the problem.