| The Science Study Series | 9 |
| Foreword | 11 |
| I. Thoughts about Thinking | 21 |
| The Reasoning Animal--Reasoning and Fun--The Kind of Questions We Have to Answer--What Kind of Reasoning Is Able to Furnish Useful Replies to Questions of This Sort?--Thinking and Reasoning--Classical Logic | |
| II. The Birth of Lady Luck | 43 |
| III. The Concept of Mathematical Probability | 53 |
| Don't Expect Too Much--Mathematical Theories and the Real World of Events--Mathematical Models--Can There Be Laws for Chance?--The Rolling of a Pair of Dice--The Number of Outcomes--Equally Probable Outcomes--Ways of Designing Models--The Definition of Mathematical Probability--A Recapitulation and a Look Ahead--Note on Terminology--Note on Other Books about Probability | |
| IV. The Counting of Cases | 83 |
| Preliminary--Compound Events--Permutations--Combinations--More Complicated Cases | |
| V. Some Basic Probability Rules | 102 |
| A Preliminary Warning--Independent Events and Mutually Exclusive Events--Converse Events--Fundamental Formulas for Total and for Compound Probability | |
| VI. Some Problems | 114 |
| Foreword--The First Problem of de Méré--The Problem of the Three Chests--A Few Classical Problems--The Birthday Problem--Montmort's Problem--Try These Yourself--Note about Decimal Expansions | |
| VII. Mathematical Expectation | 149 |
| How Can I Measure My Hopes?--Mathematical Expectation--The Jar with 100 Balls--The One-Armed Bandit--The Nicolas Bernoulli Problem--The St. Petersburg Paradox--Summary Remarks about Mathematical Expectation--Try These--Where Do We Eat? | |
| VIII. The Law of Averages | 177 |
| The Long Run--Heads or Tails | |
| IX. Variability and Chebychev's Theorem | 187 |
| Variability--Chebychev's Theorem | |
| X. Binomial Experiments | 204 |
| Binomial Experiments--Why "Binomial"?--Pascal's Arithmetic Triangle--Binomial Probability Theorem--Some Characteristics of Binomial Experiments | |
| XI. The Law of Large Numbers | 225 |
| Bernoulli's Theorem--Comments About the Classical Law of Large Numbers--Improved Central Limit Theorems--Note on Large Numbers | |
| XII. Distribution Functions and Probabilities | 241 |
| Probability Distributions--Normalized Charts--The Normal or Gaussian Distribution--What Is Normally Distributed?--The Quincunx--Other Probability Distributions, The Poisson Distribution--The Distribution of First Significant Digits | |
| XIII. Rare Events, Coincidences, and Surprising Occurrences | 278 |
| Well, What Do You Think about That!--Small Probabilities--Note on the Probability of Dealing Any Specified Hand of Thirteen Cards--Further Note on Rare Events | |
| XIV. Probability and Statistics | 304 |
| Statistics--Deduction and Induction--Sampling--What Sort of Answers Can Statistics Furnish?--The Variation of Random Samples--Questions (2) and (3): Statistical Inference--Question (4): Experimental Design | |
| XV. Probability and Gambling | 324 |
| The Game of Craps--The Ruin of the Player--Roulette, Lotteries, Bingo, and the Like--Gambling Systems | |
| XVI. Lady Luck Becomes a Lady | 349 |
| Preliminary--The Probability of an Event--Geometrical Probabilities--It Can't Be Chance!--The Surprising Stability of Statistical Results--The Subtlety of Probabilistic Reasoning--The Modern Reign of Probability--Lady Luck and the Future | |
| Index | 378 |