by David J. Eloi

Created on: July 08, 2009   Last Updated: July 13, 2009

We see that the theory of probabilities is at bottom only common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by sort of instinct, often without being able to account for it

~Pierre-Simon Laplace

The objective of mathematics is to aid man in his quest to understand nature but mathematics has also proved to be a useful tool in the pursuit of profits. The foundation for mathematics was laid by the ancient Egyptians and Babylonians then built upon later by the Greeks during the Classical period. The theory of probability came along quite a bit later in the seventeenth century and was created in the interest of mastering games of chance or gambling. Yes, gambling, throwing dice, playing cards, horse races and the like benefit from the study of probabilities and, in fact, motivated the development of this branch of mathematics.

Morris Kline in his book Mathematics for Non-mathematician describes how Jerome Cardan wrote a book during the Renaissance entitled Liber De Ludo Aleae (The Book on Games of Chance) in which advice as to how to cheat and detect cheaters when gambling was provided. The late Professor Kline who taught at New York University also provides the story of Chevalier de Mere (1653), a gambler and amateur mathematician, who elicited the help of Blaise Pascal and Pierre de Fermat to help solve problems related to games of chance. Pascal and Fermat decided to take the subject of probability further and create an entirely new mathematical science.

Kline states that the theory of probability allows business professionals and scientists alike to relinquish rough estimates for more exact probabilities. According to Charles and Corrinne Brase in Understanding Statistics determining the probability of an event involves using a number between 0 and 1 to indicate the likelihood of an event.

One definition of probabilities with equally likely outcomes is such that of n equally likely outcomes, m are favorable to the happening of a certain event, the probability of the event happening is m/n and the probability of the event failing is (n-m)/n.

Formula:

Probability = Number of outcomes favorable to event / Total number of outcomes

One example might be the likely hood of choosing a queen out of a deck of cards. Of the 52 cards or equal outcomes there are 4 possible favorable outcomes such that the probability is 4 out of 52 or 4/52 = 1/13.

The above definition of probability according to Pascal and Fermat is applicable only when future outcomes are equally likely to happen.

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