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Conditional Probability
In probability theory, conditional probability is a measure of the probability of an Event (probability theory), event occurring, given that another event (by assumption, presumption, assertion or evidence) is already known to have occurred. This particular method relies on event A occurring with some sort of relationship with another event B. In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A, or the ratio of the probabilities of both events happening to the "given" one happening (how many times A occurs rather than not assuming B has occurred): P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |