1.1 概率的历史

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.
数百年以前，人们已经使用概率来测量不确定性和可变性。概率的应用范围很广，包括医学、赌博、天气预报和法律。

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 b.c.,
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 b.c. 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.

不确定性和文明同样历史悠久。人们努力减少天气、食品供应和环境其他方面的不确定性和不良后果。赌博的历史也很长。大约在公元前3500年，利用骨骼物体（骰子的前身）的赌博游戏在埃及和其他地方广为传播。经过考古研究，在公元前2000年的坟墓中找到了立方体的骰子。从那时起，骰子的赌博游戏就广受欢迎，并且在概率论的早期发展中起到了举足轻重的作用。

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–

通常认为，概率的数学理论是由帕斯卡和费马开启的，他们解决了骰子赌博中精确的概率问题。然而，有一些骰子的组合问题是有Cardano 和伽利略解决的。

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.

自17世纪以来，概率论就在稳步发展，并且应用到各个领域上。时至今日，概率论在大工程、科学和管理领域都是非常重要的工具。许多研究人员将概率论应用在医学、气象学，卫星摄影、市场营销、地震预测、人类行为、计算机系统设计、金融，遗传学和法律等领域。在许多涉及反垄断违法或就业歧视的法律诉讼中，原告与被告双方通过运用概率论和统计学的知识，从而支撑各自的观点。