I Thoughts about Thinking
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
II The Birth of Lady Luck
III The Concept of Mathematical Probability
Don't Expect Too Much
Mathematical Theories and the Real World of Events
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
More Complicated Cases
V Some Basic Probability Rules
A Preliminary Warning
Independent Events and Mutually Exclusive Events
Fundamental Formulas for Total and for Compound Probability
VI Some Problems
The First Problem of de Méré
The Problem of the Three Chests
A Few Classical Problems
The Birthday Problem
Try These Yourself
Note about Decimal Expansions
VII Mathematical Expectation
How Can I Measure My Hopes?
The Jar with 100 Balls
The One-Armed Bandit
The Nicolas Bernoulli Problem
The St. Petersburg Paradox
Summary Remarks about Mathematical Expectation
Where Do We Eat?
VIII The Law of Averages
The Long Run
Heads or Tails
IX Variability and Chebychev's Theorem
X Binomial Experiments
Pascal's Arithmetic Triangle
Binomial Probability Theorem
Some Characteristics of Binomial Experiments
XI The Law of Large Numbers
Comments About the Classical Law of Large Numbers
Improved Central Limit Theorems
Note on Large Numbers
XII Distribution Functions and Probabilities
The Normal or Gaussian Distribution
What Is Normally Distributed?
"Other Probability Distributions, The Poisson Distribution"
The Distribution of First Significant Digits
XIII "Rare Events, Coincidences, and Surprising Occurrences"
"Well, What Do You Think about That!"
Note on the Probability of Dealing Any Specified Hand of Thirteen Cards
Further Note on Rare Events
XIV Probability and Statistics
Deduction and Induction
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
The Game of Craps
The Ruin of the Player
"Roulette, Lotteries, Bingo, and the Like"
XVI Lady Luck Becomes a Lady
The Probability of an Event
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