Synopses & Reviews
"Should I take my umbrella?" "Should I buy insurance?" "Which horse should I bet on?" Every day ― in business, in love affairs, in forecasting the weather or the stock market questions arise which cannot be answered by a simple "yes" or "no." Many of these questions involve probability. Probabilistic thinking is as crucially important in ordinary affairs as it is in the most abstruse realms of science.
This book is the best nontechnical introduction to probability ever written. Its author, the late Dr. Warren Weaver, was a professor of mathematics, active in the Rockefeller and Sloan foundations , an authority on communications and probability, and distinguished for his work at bridging the gap between science and the average citizen. In accessible language and drawing upon the widely diverse writings of thinkers like Kurt Godel, Susanne K.Langer, and Nicholas Bernoulli, Dr. Weaver explains such concepts as permutations, independent events, mathematical expectation, the law of averages, Chebychev's theorem, the law of large numbers, and probability distributions. He uses a probabilistic viewpoint to illuminate such matters as rare events and coincidences, and also devotes space to the relations of probability and statistics, gambling, and modern scientific research. Dr. Weaver writes with wit, charm and exceptional clarity. His mathematics is elementary, grasp of the subject profound, and examples fascinating. They are complemented by 49 delightful drawings by Peg Hosford. 13 tables. 49 drawings. Foreword. Index.
Synopsis
This witty, nontechnical introduction to probability elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.
Synopsis
Best nontechnical introduction. With exceptional clarity, distinguished mathematician explains law of averages, coincidences, distributions, etc. No advanced math. 49 drawings.
Synopsis
This witty, nontechnical introduction to probability elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.
About the Author
Warren Weaver: A Prolific Mind
Warren Weaver (1894-1978) was an engineer, mathematician, administrator, public advocate for science, information age visionary, and author or co-author of many books including the one on which his authorial fame mostly rests, his and Claude Shannon's epoch-making 1949 work, The Mathematical Theory of Communication.
A man with a restless intelligence, he also wrote an early seminal work on the theory of machine translation, a unique work on the publishing history of Alice in Wonderland in the many languages into which it has been translated, Alice in Many Tongues, and the book which introduced the Sputnik generation and their followers to the intricacies and enjoyment of the basic concepts of probability, Lady Luck: The Theory of Probability. This book, first published in 1963, has been a fixture on the Dover list since 1982.
From the Book:
"I say that you may at the moment be almost bored at the prospect of thinking about thinking. But this book is going to introduce you to a special way of thinking, a special brand of reasoning, which, I am confident, you will find not only useful, but fun as well. It will be about a type of thinking that, when stated boldly, seems a little strange. For we often suppose that we think with the purpose of coming to definite and sure conclusions. This book, on the contrary, deals with thinking about uncertainty."
In the Author's Own Words:
"We keep, in science, getting a more and more sophisticated view of our essential ignorance." — Warren Weaver
Table of Contents
Foreword
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
Classical Logic
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
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
Preliminary
Compound Events
Permutations
Combinations
More Complicated Cases
V Some Basic Probability Rules
A Preliminary Warning
Independent Events and Mutually Exclusive Events
Converse Events
Fundamental Formulas for Total and for Compound Probability
VI Some Problems
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
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
The Long Run
Heads or Tails
IX Variability and Chebychev's Theorem
Variability
Chebychev's Theorem
X Binomial Experiments
Binomial Experiments
"Why "Binomial"?"
Pascal's Arithmetic Triangle
Binomial Probability Theorem
Some Characteristics of Binomial Experiments
XI The Law of Large Numbers
Bernoulli's Theorem
Comments About the Classical Law of Large Numbers
Improved Central Limit Theorems
Note on Large Numbers
XII Distribution Functions and Probabilities
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"
"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
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
The Game of Craps
The Ruin of the Player
"Roulette, Lotteries, Bingo, and the Like"
Gambling Systems
XVI Lady Luck Becomes a Lady
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