The use of probability to measure uncertainty and variability dates back hundreds of years. Probability has found application in areas as diverse as medicine, gambling, weather forecasting, and the law.
The concepts of chance and uncertainty are as old as civilization itself. People have always had to cope with uncertainty about the weather, their food supply, and other aspects of their environment, and have striven to reduce this uncertainty and its effects. Even the idea of gambling has a long history. By about the year 3500 BC, games of chance played with bone objects that could be considered precursors of dice were apparently highly developed in Egypt and elsewhere. Cubical dice with markings virtually identical to those on modern dice have been found in Egyptian tombs dating from 2000 BC. We know that gambling with dice has been popular ever since that time and played an important part in the early development of probability theory.
It is generally believed that the mathematical theory of probability was started by the French mathematicians Blaise Pascal (1623–1662) and Pierre Fermat (1601–1665) when they succeeded in deriving exact probabilities for certain gambling problems involving dice. Some of the problems that they solved had been outstanding for about 300 years. However, numerical probabilities of various dice combinations had been calculated previously by Girolamo Cardano (1501–1576) and Galileo Galilei (1564-1642).
The theory of probability has been developed steadily since the seventeenth century and has been widely applied in diverse fields of study. Today, probability theory is an important tool in most areas of engineering, science, and management. Many research workers are actively engaged in the discovery and establishment of new applications of probability in fields such as medicine, meteorology, photography from satellites, marketing, earthquake prediction, human behavior, the design of computer systems, finance, genetics, and law. In many legal proceedings involving antitrust violations or employment discrimination, both sides will present probability and statistical calculations to help support their cases.
1.1.2 References¶
The ancient history of gambling and the origins of the mathematical theory of probability are discussed by David (1988), Ore (1960), Stigler (1986), and Todhunter (1865).
Some introductory books on probability theory, which discuss many of the same topics that will be studied in this book, are Feller (1968); Hoel et al. (1971); Meyer (1970); and Olkin et al. (1980). Other introductory books, which discuss both probability theory and statistics at about the same level as they will be discussed in this book, are Brunk (1975); Devore (1999); Fraser (1976); Hogg & Tanis (1997); Kempthorne & Folks (1971); Larsen & Marx (2001); Larson (1974); Lindgren (1976); Miller & Miller (1999); Mood et al. (1974); Rice (1995); and Wackerly et al. (1996).
- David, F. N. (1988). Games, Gods, and Gambling. Dover Publications.
- Ore, O. (1960). Pascal and the Invention of Probability Theory. American Mathematical Monthly, 67, 409–419.
- Stigler, S. M. (1986). The History of Statistics. Belknap Press of Harvard University Press.
- Todhunter, I. (1865). A History of the Mathematical Theory of Probability from the Time of Pascal to That of Laplace. G. E. Stechert.
- Feller, W. (1968). An Introduction to Probability Theory and Its Applications (3rd ed., Vol. 1, p. 3). John Wiley and Sons.
- Hoel, P. G., Port, S., & Stone, C. L. (1971). Introduction to Probability Theory. Houghton-Mifflin.
- Meyer, P. L. (1970). Introductory Probability and Statistical Applications (2nd ed.). Addison-Wesley.
- Olkin, I., Gleser, L. J., & Derman, C. (1980). Probability Models and Applications. Macmillan.
- Brunk, H. D. (1975). An Introduction to Mathematical Statistics (3rd ed.). Xerox College Publishing.
- Devore, J. L. (1999). Probability and Statistics for Engineering and the Sciences (5th ed.). Brooks/Cole.
- Fraser, D. A. S. (1976). Probability and Statistics. Duxbury Press.
- Hogg, R. V., & Tanis, E. A. (1997). Probability and Statistical Inference (5th ed.). Prentice-Hall.
- Kempthorne, O., & Folks, L. (1971). Probability, Statistics, and Data Analysis. Iowa State University Press.
- Larsen, R. J., & Marx, M. L. (2001). An Introduction to Mathematical Statistics and Its Applications (3rd ed.). Prentice-Hall.
- Larson, H. J. (1974). Introduction to Probability Theory and Statistical Inference (2nd ed.). John Wiley and Sons.