A short history of probability theory and its applications

Abstract

It is remarkable that a science (Probability) which began with consideration of games of chance, should have become the most important object of human knowledge.

Probability has reference partly to our ignorance, partly to our knowledge. … The Theory of chances consists in reducing all events of the same kind to a certain number of cases equally possible, that is, such that we are equally undecided as to their existence; and determining the number of these cases which are favourable to the event sought. The ratio of that number to the number of all the possible cases is the measure of the probability . …

P.S. Laplace

The true logic of this world is to be found in theory of probability.

James Clark Maxwell

This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013 marks the tricentennial anniversary of Bernoulli's law of large numbers since its posthumous publication in 1713. Special attention is given to Bayes’ celebrated theorem and the famous controversy between the Bayesian and frequentism approaches to probability and statistics. This paper is also written to pay a special tribute to Thomas Bayes since the year 2013 marks the 250th anniversary of Bayes’ celebrated work in probability and statistics, since its posthumous publication in 1763. This is followed by a short review of the modern axiomatic theory of probability first created by A.N. Kolmogorov in 1933.

Keywords:

• probability
• Bayes' theorem
• least squares
• binomial
• normal distributions and Poisson distributions 2010 AMS Mathematics Subject Classification Codes: 01A, 60-02

Acknowledgements

The authors would like to thank the referee(s) for some suggestions for the improvement of exposition of the paper. We express our grateful thanks to Dr Carroll Webber for his careful reading of the manuscript with some correction of grammatical errors. His many other suggestions also helped improve the content of the paper.