ALLAN G. BLUMAN
A SELF-TEACHING GUIDE
 |
| Probability Demystified |
I would like to thank my wife, Betty Claire, for helping me with the preparation
of this book and my editor, Judy Bass, for her assistance in its publication.
I would also like to thank Carrie Green for her error checking
and helpful suggestions.
Introduction
Probability can be defined as the mathematics of chance. Most people are
familiar with some aspects of probability by observing or playing gambling
games such as lotteries, slot machines, black jack, or roulette. However,
probability theory is used in many other areas such as business, insurance,
weather forecasting, and in everyday life.
In this chapter, you will learn about the basic concepts of probability using
various devices such as coins, cards, and dice. These devices are not used as
examples in order to make you an astute gambler, but they are used because
they will help you understand the concepts of probability.
PREFACE
‘‘The probable is what usually happens.’’ — Aristotle
Probability can be called the mathematics of chance. The theory of probability
is unusual in the sense that we cannot predict with certainty the individual
outcome of a chance process such as flipping a coin or rolling a die (singular
for dice), but we can assign a number that corresponds to the probability of
getting a particular outcome. For example, the probability of getting a head
when a coin is tossed is 1/2 and the probability of getting a two when a single
fair die is rolled is 1/6.
We can also predict with a certain amount of accuracy that when a coin is
tossed a large number of times, the ratio of the number of heads to the total
number of times the coin is tossed will be close to 1/2.
Probability theory is, of course, used in gambling. Actually, mathematicians
began studying probability as a means to answer questions about
gambling games. Besides gambling, probability theory is used in many other
areas such as insurance, investing, weather forecasting, genetics, and medicine,
and in everyday life.
What is this book about?
First let me tell you what this book is not about:
. This book is not a rigorous theoretical deductive mathematical
approach to the concepts of probability.
. This book is not a book on how to gamble.
And most important
. This book is not a book on how to win at gambling!
This book presents the basic concepts of probability in a simple,
straightforward, easy-to-understand way. It does require, however, a
knowledge of arithmetic (fractions, decimals, and percents) and a knowledge
of basic algebra (formulas, exponents, order of operations, etc.). If you need
a review of these concepts, you can consult another of my books in this
series entitled Pre-Algebra Demystified.
This book can be used to gain a knowledge of the basic concepts of
probability theory, either as a self-study guide or as a supplementary
textbook for those who are taking a course in probability or a course in
statistics that has a section on probability.
The basic concepts of probability are explained in the first two chapters.
Then the addition and multiplication rules are explained. Following
that, the concepts of odds and expectation are explained. The counting
rules are explained in Chapter 6, and they are needed for the binomial and
other probability distributions found in Chapters 7 and 8. The relationship
between probability and the normal distribution is presented in Chapter 9.
Finally, a recent development, the Monte Carlo method of simulation, is
explained in Chapter 10. Chapter 11 explains how probability can be used in
game theory and Chapter 12 explains how probability is used in actuarial
science. Special material on Bayes’ Theorem is presented in the Appendix
because this concept is somewhat more difficult than the other concepts
presented in this book.
In addition to addressing the concepts of probability, each chapter ends
with what is called a ‘‘Probability Sidelight.’’ These sections cover some of
the historical aspects of the development of probability theory or some
commentary on how probability theory is used in gambling and everyday life.
I have spent my entire career teaching mathematics at a level that most
students can understand and appreciate. I have written this book with the
same objective in mind. Mathematical precision, in some cases, has been
sacrificed in the interest of presenting probability theory in a simplified way.
Good luck!
Allan G. Bluman
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Product details
Price
|
|
|---|---|
File Size
| 2,914 KB |
Pages
|
267 p |
File Type
|
PDF format |
Print Version
| 0-07-144549-8 |
Copyright
| 2005 by The McGraw-Hill Companies, Inc |
Contents
Preface ix
Acknowledgments xi
CHAPTER 1 Basic Concepts 1
CHAPTER 2 Sample Spaces 22
CHAPTER 3 The Addition Rules 43
CHAPTER 4 The Multiplication Rules 56
CHAPTER 5 Odds and Expectation 77
CHAPTER 6 The Counting Rules 94
CHAPTER 7 The Binomial Distribution 114
CHAPTER 8 Other Probability Distributions 131
CHAPTER 9 The Normal Distribution 147
CHAPTER 10 Simulation 177
CHAPTER 11 Game Theory 187
CHAPTER 12 Actuarial Science 210
Final Exam 229
Answers to Quizzes and Final Exam 244
Appendix: Bayes’ Theorem 249
Index 255
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