The Meaning of Probability

It is generally recognized that the theory of probability should no longer be treated as adjunct to a course in statistics or reliability but must be taught as a basic discipline, a prerequisite for several courses. In teaching the subject one must overcome an initial obstacle. In public schools and even in colleges, students learn that the universe evolves according to deterministic laws that specify completely its future, and a probabilistic description of its evolution is needed only because of our ignorance. This deep-rooted skepticism in the validity of probabilistic results can be overcome only by a proper interpretation of the meaning of probability. In this paper we attempt to present and analyze the various definitions and their role in a probability course.