Probability and Expected Value: From High School to the Olympiads

A rigorous and accessible journey through expected value - from the definition to Markov chains, from the gambler's ruin to the dangers of betting. Every formula is proved, with problems from entrance exams and olympiads - IME, ITA, OBM - plus a chapter with 107 solved multiple-choice questions. Born from the author's master's dissertation at PUC-Rio on the teaching of Probability and Expected Value, the book is structured around fascinating themes. Part I (Foundations) develops, in sequence, the concepts of probability, conditional probability, total probability (and Bayes), expected value and variance. Part II brings solved expected-value problems, including the geometric distribution, the harmonic number and the elegant Coupon Collector's Problem. Part III solves, in detail, problems usually stated without solution in the classroom. Part IV gathers entrance-exam and olympiad exercises, organized by the same chapters as the Foundations. May the clarity of numbers help you protect your own wallet - and achieve the highest grades.