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Making good decisions under conditions of uncertainty - which is the norm - requires a sound appreciation of the way random chance works. As analysis and modelling of most aspects of the world, and all measurement, are necessarily imprecise and involve uncertainties of varying degrees, the understanding and management of probabilities is central to much work in the sciences and economics.
In this "Very Short Introduction", John Haigh introduces the ideas of probability and different philosophical approaches to probability, and gives a brief account of the history of development of probability theory, from Galileo and Pascal to Bayes, Laplace, Poisson, and Markov. He describes the basic probability distributions, and goes on to discuss a wide range of applications in science, economics, and a variety of other contexts such as games and betting. He concludes with an intriguing discussion of coincidences and some curious paradoxes.
2: The workings of probability
3: Historical sketch
4: Chance experiments
5: Making sense of probabilities
6: Games people play
7: Applications in science and operations research
8: Other applications
9: Curiosities and dilemmas
Appendix - Answers to questions posed
John Haigh is a mathematics tutor at the University of Sussex and has written many papers on probability. He is the author of three books, including "Taking Chances" (2003).