If
[math]A
[/math] and
[math]B \href{/cs2800/wiki/index.php/%E2%8A%86}{⊆} \href{/cs2800/wiki/index.php/S}{S}
[/math] are
events, then the
conditional probability of
[math]B
[/math] given [math]A
[/math] (written
[math]\href{/cs2800/wiki/index.php/Pr}{Pr}(B \href{/cs2800/wiki/index.php/%5Cmid}{\mid} A)
[/math]) is given by
[math]\href{/cs2800/wiki/index.php/Pr}{Pr}(B \href{/cs2800/wiki/index.php/%5Cmid}{\mid} A) \href{/cs2800/wiki/index.php/Definition}{:=} \frac{\href{/cs2800/wiki/index.php/Pr}{Pr}(B \href{/cs2800/wiki/index.php/%E2%88%A9}{∩} A)}{\href{/cs2800/wiki/index.php/Pr}{Pr}(A)}
[/math]
