Probability Theory

The branch of mathematics known as probability theory was inspired by gambling problems. The earliest work was performed by Girolamo Cardano (1501-1576) an Italian mathematician, physician, and gambler. In his manual Liber de Ludo Aleae, Cardano discusses many of the basic concepts of probability complete with a systematic analysis of gambling problems. Unfortunately, Cardano's work had little effect on the development of probability because his manual, which did not appeared in print until 1663, received little attention.

In 1654, another gambler named Chevalier de Méré created a dice proposition which he believed would make money. He would bet even money that he could roll at least one 12 in 24 rolls of two dice. However, when the Chevalier began losing money, he asked his mathematician friend Blaise Pascal (1623-1662) to analyze the proposition. Pascal determined that this proposition will lose about 51% of the time. Inspired by this proposition, Pascal began studying more of these types of problems. He discussed them with another famous mathematician, Pierre de Fermat (1601-1665) and together they laid the foundation of probability theory.

Probability theory is concerned with determining the relationship between the number of times a certain event occurs and the number of times any event occurs. For example, the number of times a head will appear when a coin is flipped 100 times. Determining probabilities can be done in two ways; theoretically and empirically. The example of a coin toss helps illustrate the difference between the two approaches. Using a theoretical approach, we reason that in every flip there are two possibilities, a head or a tail. By assuming each event is equally likely, the probability that the coin will end up heads is 1/2 or 0.5. The empirical approach does not use assumption of equal likeliness. Instead, an actual coin flipping experiment is performed and the number of heads is counted. The probability is then equal to the number of heads divided by the total number of flips.