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Probability theory is the mathematical study of probability.
The basic theorems of probability can be developed from the probability axioms and set theory. The following assumes that there are only countably many elementary events (which is not the case for many common probability distributions, such as the normal distribution).
The formulae below express the same ideas in algebraic terms.
OR
Where E_{i} is any event in both A_{1} and A_{2}.
Where E_{i} is any event in either A_{1} or A_{2}.
The probability of some event happening knowing that another event happened before can be computed using conditional probability.
See also: probability, probability axioms, probability distribution, likelihood
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