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Given two events A and B from the sigma-field of a probability space, with the unconditional probability of B being greater than zero (i.e., P(B) > 0), the conditional probability of A given B (()) is the probability of A occurring if B has or is assumed to have happened. [5]
Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P ( A ∣ B ) {\displaystyle P(A\mid B)} , and is read "the probability of A , given B ".
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
Thus the conditional probability P(B |A) is turned into simple probability P(B → A) by replacing Ω, the sample space of all ordinary outcomes, with Ω*, the sample space of all sequences of ordinary outcomes, and by identifying conditional event A → B with the set of sequences where the first (A ∧ B)-outcome comes before the first (A ∧ ...
Given two jointly distributed random variables and , the conditional probability distribution of given is the probability distribution of when is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value of as a parameter.
Two events, A and B are said to be mutually exclusive or disjoint if the occurrence of one implies the non-occurrence of the other, i.e., their intersection is empty. This is a stronger condition than the probability of their intersection being zero. If A and B are disjoint events, then P(A ∪ B) = P(A) + P(B). This extends to a (finite or ...
The probability is sometimes written to distinguish it from other functions and measure P to avoid having to define "P is a probability" and () is short for ({: ()}), where is the event space, is a random variable that is a function of (i.e., it depends upon ), and is some outcome of interest within the domain specified by (say, a particular ...
In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.
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