Conditional probability is the probability of some event A, given the occurrence of some other event B. Conditional probability is written P(A|B), and is read "the probability of A, given B". Joint probability is the probability of two events in conjunction.

That is, it is the probability of both events together. The joint probability of A and B is written or Marginal probability is then the unconditional probability P(A) of the event A; that is, the probability of A, regardless of whether event B did or did not occur. If B can be thought of as the event of a random variable X having a given outcome, the marginal probability of A can be obtained by summing (or integrating, more generally) the joint probabilities over all outcomes for X.

For example, if there are two possible outcomes for X with corresponding events B and B', this means that . This is called marginalization. In these definitions, note that there need not be a causal or temporal relation between A and B.

A may precede B or vice versa or they may happen at the same time. A may cause B or vice versa or they may have no causal relation at all. Notice, however, that causal and temporal relations are informal notions, not belonging to the probabilistic framework.

They may apply in some examples, depending on the interpretation given to events.

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