The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation. It describes how to set up and analyse models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. This popular second edition textbook contains many worked examples and several chapters have been updated and expanded. Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument. "Probability Models" is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.

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. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

How does mathematics impact everyday events? Through concrete examples from business, sport, games, computing, and society, this book explores the mathematics underpinning our everyday lives. The examples covered in the book include game shows, internet search engines, mortgage payments, drug testing, soccer tournaments, social inequality, voting, and much more. Throughout, the reader's mathematical knowledge is broadened with new topics such as differential equations, eigenvalues of matrices, linear programming, and modular arithmetic. Fully worked examples illustrate the ideas discussed and each chapter includes exercises to develop the reader's understanding. This new edition has been thoroughly updated, and includes a completely new chapter on applications of mathematics to computing. Mathematics in Everyday Life supports beginning university students in science and engineering by offering extra practice in calculus, linear algebra, geometry, trigonometry, elementary number theory, and probability. Students whose degree course includes writing an extended mathematical essay will find many suitable topics here, with pointers to extend and develop the material.

What are the odds against winning the Lottery, making money in a casino, or backing the right horse? Every day, people make judgements on these matters and face other decisions that rest on their understanding of probability: buying insurance, following medical advice, carrying an umbrella. Yet many of us have a frightening ignorance of how probability works. Taking Chances presents an entertaining and fascinating exploration of probability, revealing traps and fallacies in the field. It describes and analyses a remarkable variety of situations where chance plays a role, including football pools, the Lottery, TV games, sport, cards, roulette, coins, and dice. This new edition has been fully updated, and includes information on "Who Wants to be a Millionaire?" and "The Weakest Link", plus a new chapter on Probability for Lawyers.