##
**Fat chance. Probability from 0 to 1.**
*(English)*
Zbl 1423.00005

Cambridge: Cambridge University Press (ISBN 978-1-108-48296-7/hbk; 978-1-108-72818-8/pbk; 978-1-108-61027-8/ebook). xi, 200 p. (2019).

From the cover of the book: “In a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion.

This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Readers at any level are equipped to consider probability at large and work through exercises on their own.”

The book is structured in a Preface, 14 chapters (divided into 68 subchapters), Appendix A: Boxed formulas, Appendix B: Normal table, Index:

Part I. “Counting” with the Chapter 1. Simple counting; Chapter 2. The multiplication principle; Chapter 3. The subtraction principle; Chapter 4. Collection; Chapter 5. Games of chance; “Interlude” with the Chapter 6. Pascal’s triangle and the binomial theorem; Chapter 7. Advanced counting.

Part II. “Probability” with the Chapter 8. Expected value; Chapter 9. Conditional probability; Chapter 10. Life’s like that: unfair coins and loaded dice; Chapter 11. Geometric probability.

Part III. “Probability at large” with the Chapter 12. Games and their payoffs; Chapter 13. The normal distribution; Chapter 14. Don’t try this at home.

Almost all subchapters finished with Exercises. The Index contains more than 110 items. However the book contains no references.

A critical remark: In the book the term “random variable” is missing. Here the authors use the term “game \(G\)”, later the term “expected value of \(G\)” with notation \(\text{ev}(G)\) and the term “variance of \(G\)” with the notation \(\text{var}(G)\). The values of \(G\) are the “payoffs”. The authors use e.g. the notation \(G+G+G\) for the sum of three independent and identically distributed random variables \(G\) and omit the notation e.g. \(G1+G2+G3\). Thus they explain e.g. that \(G+G\) means “the same game \(G\) is played twice” and \(2G\) means “the game \(G\) with payoffs doubled”. Later the notation \(G+G+G+G=G(4)\) and so on.

The book can be recommended to all readers without deeper knowledge in elementary statistics and probability, who are interested in this field. For interactive material, see https://harvardx.link/fat-chance.

This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Readers at any level are equipped to consider probability at large and work through exercises on their own.”

The book is structured in a Preface, 14 chapters (divided into 68 subchapters), Appendix A: Boxed formulas, Appendix B: Normal table, Index:

Part I. “Counting” with the Chapter 1. Simple counting; Chapter 2. The multiplication principle; Chapter 3. The subtraction principle; Chapter 4. Collection; Chapter 5. Games of chance; “Interlude” with the Chapter 6. Pascal’s triangle and the binomial theorem; Chapter 7. Advanced counting.

Part II. “Probability” with the Chapter 8. Expected value; Chapter 9. Conditional probability; Chapter 10. Life’s like that: unfair coins and loaded dice; Chapter 11. Geometric probability.

Part III. “Probability at large” with the Chapter 12. Games and their payoffs; Chapter 13. The normal distribution; Chapter 14. Don’t try this at home.

Almost all subchapters finished with Exercises. The Index contains more than 110 items. However the book contains no references.

A critical remark: In the book the term “random variable” is missing. Here the authors use the term “game \(G\)”, later the term “expected value of \(G\)” with notation \(\text{ev}(G)\) and the term “variance of \(G\)” with the notation \(\text{var}(G)\). The values of \(G\) are the “payoffs”. The authors use e.g. the notation \(G+G+G\) for the sum of three independent and identically distributed random variables \(G\) and omit the notation e.g. \(G1+G2+G3\). Thus they explain e.g. that \(G+G\) means “the same game \(G\) is played twice” and \(2G\) means “the game \(G\) with payoffs doubled”. Later the notation \(G+G+G+G=G(4)\) and so on.

The book can be recommended to all readers without deeper knowledge in elementary statistics and probability, who are interested in this field. For interactive material, see https://harvardx.link/fat-chance.

Reviewer: Ludwig Paditz (Dresden)

### MSC:

00A09 | Popularization of mathematics |

97A80 | Popularization of mathematics (MSC2010) |

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |

97K50 | Probability theory (educational aspects) |