Definition:Conditional probability

From CS2800 wiki
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]