Let us now examine the various ways in which probabilities are determined. Two broad categories of probabilities are typically recognized: objective probability versus subjective probability. Moreover, under the objective heading, we have the classical approach versus the empirical determination of probability.

The classical approach utilities a priori (before the fact) knowledge, that is, we can determine a theoretical probability by counting points or simple events within S. Clearly, this approach utilizes the physical structure of an implied experiment and is used when we have n equiprobable simple events in S.

An empirical probability utilizes a posteriori (after the fact) knowledge; it makes use of accumulated or historical experience or is determined by actually performing a random experiment. That is, we can compute the relative frequency of an event via a random experiment. Specifically, if is an event for a random experiment and if that experiment is repeated times and is observed in of the repetitions, then the relative frequency of event is ...

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