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 |