Introduction to Probability: (Dover Books on Mathema 1.4tics)

Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more. For centuries, humans lived with the "uncertainties" of everyday life, unaware of probability theory and how it might be applied to the solution of simple problems of daily living or used to study the laws of nature. It was not until the advent of the scientific method with its emphasis on observation and experimentation that people began to think about the role probability might play in areas of life that once seemed ruled by blind chance. Today, of course, probability theory is the basis of statistics and game theory, and can be immensely useful to anyone engaged in business, the social and physical sciences, and many other areas of endeavor. This volume demonstrates that the study of probability can be fun, challenging, and relevant - both to daily life and to modern scientific thought. Lucid, well-written chapters introduce the reader to the concept of possibilities, including combinations and permutations; probabilities, expectations (utility, decision making, more), events, rules of probability, conditional probabilities, probability distributions, the law of large numbers, including Chebyshev's theorem, and more. Numerous exercises throughout the text are designed to reinforce the methods and ideas explained in the book. Answers to the odd-numbered exercises are provided. A bibliography and summary round out this valuable introduction that will be of great help to anyone engaged in business, social sciences, statistical work, game theory, or just the business of living.

Table of Contents:
INTRODUCTION 1 POSSIBILITIES Introduction Tree Diagrams Multiplication Rules Permutations Factorials Indistinguishable Objects Combinations Binomial Coefficients 2 PROBABILITIES Introduction The Classical Concept Probabilities and Odds The Frequency Interpretation Subjective Probabilities Summary 3 EXPECTATIONS Introduction Mathematical Expectation Expectations and Subjective Probabilities Utility Decision Making 4 EVENTS Introduction The Sample Space Events Compound Events The Number of Elements in a Set 5 RULES OF PROBABILITY Introduction The Postulates of Probability Probability Measures Some Further Rules General Addition Rules 6 CONDITIONAL PROBABILITIES Introduction Conditional Probability Multiplication Rules Rule of Elimination Bayes' Rule 7 PROBABILITY DISTRIBUTIONS Introduction Probability Functions The Mean The Binomial Distribution Binomial Tables A Bayesian Application The Hypergeometric Distribution The Geometric Distribution The Multinomial Distribution 8 THE LAW OF LARGE NUMBERS Introduction The Standard Deviation Chebyshev's Theorem The Law of Large Numbers Technical Note SUMMARY BIBLIOGRAPHY TABLES ANSWERS TO ODD-NUMBERED EXERCISES INDEX