Lady Luck The Theory of Probability

by Weaver, Warren

• ISBN13: 9780486243429
• ISBN10: 0486243427
• Format: Paperback
• Copyright: 1982-08-01
• Publisher: Dover Publications

Summary

Everyday questions such as "Should I take my umbrella?" involve probability, a topic important in daily life and in science. This witty, nontechnical introduction to the subject elucidates such concepts as permutations, independent events, mathematical expectation, the law of averages and more. No advanced math required. 49 drawings.

Author Biography

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