Wiktionary
n. (context mathematics English) The mathematical study of probability (the likelihood of occurrence of random events in order to predict the behavior of defined systems).
WordNet
n. the branch of applied mathematics that deals with probabilities
Wikipedia
Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion.
It is not possible to predict precisely results of random events. However, if a sequence of individual events, such as coin flipping or the roll of dice, is influenced by other factors, such as friction, it will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.
As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics.
Usage examples of "probability theory".
Point defense stopped ninety-five percent of the incoming fire short of Goeben, yet simple probability theory said at least some birds had to get through, and the battlecruiser heaved as they wiped away her shields and tore at her armor.
But spending three or four grades practising once again the addition, subtraction, multiplication and division of fractions would bore anyone, and the tragedy is that, say, elementary probability theory is within reach of these students.
No matter how sharp a guy's probability theory might be, no matter how perceptive his psychology, if he believes even a tiny bit in luck then he is a loser at heart.
Rodricks, still very much alive, lectured in advanced probability theory at Edinburgh University.
It is a difficult concept to explain to anyone not versed in the magic arts and probability theory as well, but I'll try and boil it down.