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 $\condprob A B$, 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.

Technical Note

The $\LaTeX$ code for \(\condprob {A} {B}\) is \condprob {A} {B} .

When the arguments are single characters, it is usual to omit the braces:

\condprob n p