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Probability theory is a well-established branch of mathematics that finds applications in a wide area of scholarly activities such as in physics, chemistry, geology, medicine, economics, sociology, engineering, operation research, etc. With his insightful exploration of the probabilistic connection between philosophy and the history of science, John Maynard Keynes, perhaps the best known of economists, breathed new life in the study of both these disciplines. His A Treatise on Probability is an outstanding mathematical work and is widely considered as an important contribution to the theory regarding the logical probability of proportions. What Keynes wrote is sacrosanct and has been retained in this book. His original book is in 31 chapters. In order to facilitate updating, we have combined some chapters and presented it in 26 chapters and converted it into third person from the original first person, keeping in view the modern trend. We have added important developments that have taken place since Keynes wrote the book, to provide updated material to the students and teachers of various disciplines. The book is divided into five parts. Part-I provides fundamental ideas on probability. Part-II contains fundamental theorems. Part-III deals with induction and analogy. Part-IV throws light on some philosophical applications of probability, while Part-V relates to the foundations of statistical inference. Bibliography has been updated by including more books. Index also stands revised and updated. Exclusive chapters ‘Practice Problems’ have been added in each part except Part-IV, containing a large number of solved exercises providing plenty of opportunity to the students for practicing skills and developing a sound understanding of the subject. Unsolved exercises have been given under ‘Test Yourself’. The book with updated matter and in its present layout will be useful for students and teachers of various disciplines including economics, physical sciences, engineering, geology, statistics, economics and sociology. About the Author John Maynard Keynes was a keen student of mathematics and got his first class B.A. in Mathematics in 1904. After resigning from civil service in 1908 he returned to Cambridge and worked on probability theory. In 1911 he was made the editor of the Economic Journal. Keynes’ ideas have profoundly influenced the theory and practice of modern macroeconomics, as well as the economic policies of governments. He delved deeply into the causes of business cycles and advocated the use of fiscal and monetary measures to mitigate the adverse effects of economic recessions. His ideas are the basis for the school of thought known as Keynesian economics and its various offshoots. He is said to have spearheaded a revolution in economic thinking, overturning the older ideas of neoclassical economics. Keynes made path-breaking contribution to the logic of probability, and was the first scholar in history to explicitly emphasize the importance of internal estimates in decision making. K.R. Gupta is a well-known economist. He has studied in-depth mathematical and economics statistics. He has published over twenty books and contributed more than hundred papers in reputed journals, being published in India and abroad. The books written by him include Inflation: Issues and Concerns; Advanced Microeconomics (2 vols.); Advanced Macroeconomics (2 vols.); Economic Growth Models; Global Financial Crisis (3 vols.); International Economics (2 vols.); Economics of Development and Planning (2 vols.); and Indian Economy (3 vols., co-authored). Table of Contents Preface Volume - I Part-I Fundamental Ideas 1. Introduction 2. Probability: The Study of Chances 3. The Measurement of Probabilities 4. The Frequency Theory of Probability 5. Practice Problems Part-II Fundamental Theorems 6. Theorems of Probability 7. Probability and Inference 8. Measurement and Approximation of Probabilities 9. Problems in Inverse Probability 10. Practice Problems Part-III Induction and Analogy 11. The Nature of Argument by Analogy 12. Pure Induction 13. The Nature of Inductive Argument Continued 14. The Justification of These Methods 15. Some Historical Notes on Induction