Table of Contents for Lady Luck

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