1. The ordinary treatment of probability begins with the assumption that the chance that a certain event will occur is known, and proceeds to solve the problems that arise from the combination of events or the repetition of a particular experiment; it proves that a certain result is more likely to occur from experiment than any other, that a result based on a limited number of trials is unlikely to differ greatly from the expected result, and that the proportional deviation from the most probable result will generally decrease as the number of trials is increased.

Experiments can easily be made to show that the theoretical method leads to results which can be realized in practice when the probabilities can be estimated accurately beforehand; for example, various trials have been made with coin tossing in which it has been found that if five coins are tossed together and the number of them coming down ‘heads’ is recorded, then the distribution of the cases will agree with the binomial expansion (½+½)5 as the ordinary theory leads us to expect. Sequences of ‘heads’ or ‘tails’ form a series approximating to the geometrical progression with a common ratio of ½, and the drawing of cards from a pack gives a result closely agreeing with the numbers that theoretical work suggests.