To scientists, on the other hand, "frequentist probability" is just what philosophers call physical (or objective) probability.

Spiegelhalter showed that while frequentist probability did not lend itself to expert systems, Bayesian probability most certainly did.

Note that all of the above probabilities are subjective Bayesian probabilities, rather than frequentist probabilities in the classical sense.

Some of the confusion in the literature undoubtedly arises because the writers are using different concepts of probability, in particular, Bayesian versus frequentist probability.

For the frequentist a hypothesis is a proposition (which must be either true or false), so that the frequentist probability of a hypothesis is either one or zero.

Frequentist probability or frequentism is the standard interpretation of probability; it defines an event's probability as the limit of its relative frequency in a large number of trials.

Later editions added material on enumerative combinatorics (the numbers of ways of arranging items into groups with various constraints), derangements, frequentist probability, life expectancy, and the fairness of bets, among other topics.

The most popular version of objective probability is frequentist probability, which claims that the probability of a random event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment.

(Interpreting probability in a context where it is only possible to draw one sample from a distribution is problematic in frequentist probability but not in Bayesian probability, which is not defined in terms of the frequency of repeated events.)