Probability

Abstract

The ideas of probability are introduced using experiments. Examples are constructed in which the outcomes are equally likely, but the events contain different numbers of outcomes. Such nonuniform experiments are constructed using familiar objects: dice, coins, and playing cards. Stochastic processes, sequences of events where later events depend on the outcome of earlier events, are analyzed using tree diagrams. The earlier work on the theory of counting is applied to probability problems.

Conditional probabilities are defined, and tree diagrams are used there also. Bayes’ formula is introduced, and its applications are explored. The well-known “Monty Hall Problem” is analyzed.