Probability and chance in the theory of statistics

Abstract 1. The distinction between probability and chance.—Probability is of fundamental importance in statistical theory, which indeed we may regard merely as part of the mathematical theory of probability; yet statisticians still differ widely in opinion, among themselves as well as with others, on what it means and on how it should be used. One point that is therefore worth stressing is the distinction between probability and chance. Chance is naturally included in the wider field of probability, but at times some confusion seems to have arisen through a failure to distinguish between the two. This confusion has been related also to the fact that the probability of an event is not unique, but must depend on the data on which it is based. It is of more importance here to indicate the difference in meaning between probability and chance than to define each term individually. There is much to be said for leaving probability as an undefined concept, particularly as all attempts at definition can be criticized in one way or another ; and it will thus be assumed sufficient to say* that the probability P of a proposition or of an event a, on a set of data or premisses d, is the degree of rational belief in a, given d.