Uncertainty, Intuition, and Expectation

Abstract

Probability is an everyday notion. This is shown by the number of common words related to the idea: chance, random, hazard, fortune, likelihood, odds, uncertainty, expect, believe. Nevertheless, as with many concepts for which we have a strong but rather vague intuition, the idea of probability has taken some time to formalize. It was in the study of games of chance (such as card games and the tossing of dice) that the early attempts at formalization were made, with the understandable motive of determining one’s chances of winning. In these cases the basis of formalization was fairly clear, because one can always work from the fact that there are a number of elementary situations (such as all the possible deals in a card game) which can be regarded as ‘equally likely’. However, this approach fails in the less tangible problems of physical, economic and human life which we should like to consider, and of which we shall give a few examples below.