The Pleasures of Probability

This introduction to fundamental ideas in classical probability is written for an audience ranging from mathematical amateurs to scientists, from students to professional mathematicians. Includes illustrative problems, with answers at the end of the book.

The purpose of this book is to introduce the basic notions of probability through the discussion of a variety of problems and applications. The most important feature is the attempt to explain fundamental ideas in classical probability to non-specialists whose only prerequisite is algebra. The book can be used as a text for a first course in probability. Each chapter ends with a few problems with answers at the end of the book.

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The purpose of "The Pleasures of Probability" is to introduce some of the most fundamental ideas in classical probability to a fairly general audience - reaching from mathematical amateurs to scientists, from students to professional mathematicians. The only prerequisites required are a decent background in elementary algebra and an interest in discussions of a variety of problems and applications in probability. The style is informal, and the chapters are more like essays on a particular topic than textbook treatments. Even well-known problems are often covered in more depth than usual in order to illustrate underlying ideas. The book can be used as a text for a first course in probability or as a companion to a text. Each chapter ends with a few problems, the answers to which are given at the end of the book.

Contenu
1: Cars, Goats, and Sample Spaces. 2: How to Count: Birthdays and Lotteries. 3: Conditional Probability: From Kings to Prisoners. 4: The Formula of Thomas Bayes and Other Matters. 5: The Idea of Independence, with Applications. 6: A Little Bit About Games. 7: Random Variables, Expectations, and More About Games. 8: Baseball Cards, The Law of Large Numbers, and Bad News for Gamblers. 9: From Traffic to Chocolate Chip Cookies with the Poisson Distribution. 10: The Desperate Case of the Gambler's Ruin. 11: Breaking Sticks, Tossing Needles, and More: Probability on Continuous Sample Spaces. 12: Normal Distribution, and Order from Diversity via the Central Limit Theorem. 13: Random Numbers: What They Are and How to Use Them. 14: Computers and Probability. 15: Statistics: Applying Probability to Make Decisions. 16: Roaming the Number Line with a Markov Chain: Dependence. 17: The Brownian Motion, and Other Processes in Continuous Time.