Quantitative Methods: An Introduction for Business Management

5

Probability Theories

Any book on quantitative methods includes a chapter on probability theory, and this one is no exception. However, the careful reader should wonder why this chapter's title mentions probability theories. In Section 5.1 we show that probability, like uncertainty, is a rather elusive concept. Descriptive statistics suggests the concept of probabilities as relative frequencies, but we may also interpret probability as plausibility related to a state of belief. The origin of the mathematical approach to probability can be traced back to Jacob Bernoulli, Thomas Bayes, and Pierre-Simon Laplace. Bernoulli's Ars Conjectandi (The Art of Conjecture) was published 8 years after his death in 1713, and Laplace published his Théorie analytique des probabilités in 1812. More recently, the axiomatic approach due to Andrei Nikolaevich Kolmogorov (1933) was proposed and has become a sort of standard approach to probability. We will follow the last approach in this and subsequent chapters, because it suits our purpose very well, but it is always healthy to keep in mind that “standard” does not mean “always the best.” We come back to such issues in Chapter 14, while in this chapter we first introduce the axiomatic approach to probability theory in Section 5.2, laying down the fundamental concepts of events and probability measures, along with a set of basic rules of the game in order to work with probabilities in a sensible and consistent manner. In Section 5.3 we introduce conditional ...