Probability is the likelihood or chance that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

Interpretations

main: Probability interpretations

The word probability does not have a consistent direct definition. In fact, there are two broad categories of probability interpretations:

1. Frequentists talk about probabilities only when dealing with well defined random experiments. The probability of a random event denotes the relative frequency of occurrence of an experiment's outcome, when repeating the experiment. Frequentists consider probability to be the relative frequency "in the long run" of outcomes.
2. Bayesians, however, assign probabilities to any statement whatsoever, even when no random process is involved. Probability, for a Bayesian, is a way to represent an individual's degree of belief in a statement, given the evidence.

Prehistory and Etymology

Probability has an interesting etymology. Its meaning today is almost the opposite of the meaning of the word from which it originated. Before the seventeenth century, legal evidence in Europe was considered to greater weight if a person testifying had “probity”. “empirical evidence” was barely a concept. Probity was a measure of authority, so evidence came from authority. A noble person had probity. Yet today, probability is the very measure of the weight of empirical evidence in science, arrived at from inductive or statistical inference.

History

See: Statistics The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in those problems only arose much later.

According to Richard Jeffrey, "Before the middle of the seventeenth century, the term 'probable' (Latin probabilis) meant approvable, and was applied in that sense, univocally, to opinion and to action. A probable action or opinion was one such as sensible people would undertake or hold, in the circumstances."Jeffrey, R.C., Probability and the Art of Judgment, Cambridge University Press. (1992). pp. 54-55 . ISBN 0-521-39459-7

Aside from some elementary considerations made by Girolamo Cardano in the 16th century, the doctrine of probabilities dates to the correspondence of Pierre de Fermat and Blaise Pascal (1654). Christiaan Huygens (1657) gave the earliest known scientific treatment of the subject. Jakob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's Doctrine of Chances (1718) treated the subject as a branch of mathematics. See Ian Hacking's The Emergence of Probability for a history of the early development of the very concept of mathematical probability.