Includes bibliographical references and index.

Print version record.

2.2 Set Theory Review2.2.1 Coding Digression; 2.2.2 Sizes of Infinity and Probabilities; 2.2.3 Open and Closed Sets; 2.3 Outcome Spaces, Events, and the Axioms of Probability; 2.4 Axioms of Probability; 2.5 Basic Probability Rules; 2.5.1 Law of Total Probability; 2.5.2 Probabilities of Unions; 2.5.3 Probabilities of Inclusions; 2.6 Probability Spaces and [sigma]-algebras; 2.7 Appendix: Experimentally Finding Formulas; 2.7.1 Product Rule for Derivatives; 2.7.2 Probability of a Union; 2.8 Summary; 2.9 Exercises; 3 Counting I: Cards; 3.1 Factorials and Binomial Coefficients.

Cover; Title; Copyright; CONTENTS; Note to Readers; How to Use This Book; I General Theory; 1 Introduction; 1.1 Birthday Problem; 1.1.1 Stating the Problem; 1.1.2 Solving the Problem; 1.1.3 Generalizing the Problem and Solution: Efficiencies; 1.1.4 Numerical Test; 1.2 From Shooting Hoops to the Geometric Series; 1.2.1 The Problem and Its Solution; 1.2.2 Related Problems; 1.2.3 General Problem Solving Tips; 1.3 Gambling; 1.3.1 The 2008 Super Bowl Wager; 1.3.2 Expected Returns; 1.3.3 The Value of Hedging; 1.3.4 Consequences; 1.4 Summary; 1.5 Exercises; 2 Basic Probability Laws; 2.1 Paradoxes.

3.1.1 The Factorial Function3.1.2 Binomial Coefficients; 3.1.3 Summary; 3.2 Poker; 3.2.1 Rules; 3.2.2 Nothing; 3.2.3 Pair; 3.2.4 Two Pair; 3.2.5 Three of a Kind; 3.2.6 Straights, Flushes, and Straight Flushes; 3.2.7 Full House and Four of a Kind; 3.2.8 Practice Poker Hand: I; 3.2.9 Practice Poker Hand: II; 3.3 Solitaire; 3.3.1 Klondike; 3.3.2 Aces Up; 3.3.3 FreeCell; 3.4 Bridge; 3.4.1 Tic-tac-toe; 3.4.2 Number of Bridge Deals; 3.4.3 Trump Splits; 3.5 Appendix: Coding to Compute Probabilities; 3.5.1 Trump Split and Code; 3.5.2 Poker Hand Codes; 3.6 Summary; 3.7 Exercises.

4 Conditional Probability, Independence, and Bayes' Theorem4.1 Conditional Probabilities; 4.1.1 Guessing the Conditional Probability Formula; 4.1.2 Expected Counts Approach; 4.1.3 Venn Diagram Approach; 4.1.4 The Monty Hall Problem; 4.2 The General Multiplication Rule; 4.2.1 Statement; 4.2.2 Poker Example; 4.2.3 Hat Problem and Error Correcting Codes; 4.2.4 Advanced Remark: Definition of Conditional Probability; 4.3 Independence; 4.4 Bayes' Theorem; 4.5 Partitions and the Law of Total Probability; 4.6 Bayes' Theorem Revisited; 4.7 Summary; 4.8 Exercises; 5 Counting II: Inclusion-Exclusion.

5.1 Factorial and Binomial Problems5.1.1 "How many" versus "What's the probability"; 5.1.2 Choosing Groups; 5.1.3 Circular Orderings; 5.1.4 Choosing Ensembles; 5.2 The Method of Inclusion-Exclusion; 5.2.1 Special Cases of the Inclusion-Exclusion Principle; 5.2.2 Statement of the Inclusion-Exclusion Principle; 5.2.3 Justification of the Inclusion-Exclusion Formula; 5.2.4 Using Inclusion-Exclusion: Suited Hand; 5.2.5 The At Least to Exactly Method; 5.3 Derangements; 5.3.1 Counting Derangements; 5.3.2 The Probability of a Derangement; 5.3.3 Coding Derangement Experiments.

For students learning probability, its numerous applications, techniques, and methods can seem intimidating and overwhelming. That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly textbook helps students comfortably navigate probability's terrain and achieve positive results. The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement--both in the textbook and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus. The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses. A helpful introduction to probability or a perfect supplement for a courseNumerous worked-out examplesLectures based on the chapters are available free onlineIntuition of problems emphasized first, then technical proofs givenAppendixes review proof techniquesRelaxed, conversational approach.

In English.

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