Definition:Conditional Probability

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Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events of $\EE$.

We write the conditional probability of $A$ given $B$ as $\map \Pr {A \mid B}$, and define it as:

the probability that $A$ has occurred, given that $B$ has occurred.

Also see

  • Results about conditional probabilities can be found here.