In this chapter we introduce the basic terminology of probability theory. The notions of independence, distribution, and expected value are studied in more detail later, but it is hard to discuss examples without them, so we introduce them quickly here.

Outcomes, events, and probability

The subject of probability can be traced back to the 17th century when it arose out of the study of gambling games. As we see, the range of applications extends beyond games into business decisions, insurance, law, medical tests, and the social sciences. The stock market, “the largest casino in the world,” cannot do without it. The telephone network, call centers, and airline companies with their randomly fluctuating loads could not have been economically designed without probability theory. To quote Pierre-Simon, marquis de Laplace from several hundred years ago:

In order to address these applications, we need to develop a language for discussing them. Euclidean geometry begins with the notions of point and line. The corresponding basic object of probability is an experiment: an activity or procedure that produces distinct, well-defined possibilities called outcomes.