# Conditional Probability Formula

If the probability of any event depends on the occurrence of some other event then, it is called conditional probability. Suppose “x” is the event. Event “X” is called conditional probability if it depends on the occurrence of some other event say “y”

Mathematically, it can be written as;

$small bg_black P(X/Y) = frac{P(Xcap Y)}{P(Y)}$

P(X/Y) can read as: The probability of “X” when event “Y” has already occurred.

## Formula Explanation

If the above case is considered, then event “y” is the additional information that has already occurred. When this kind of information is given then the sample space not remain the same. Usually in practice already occurred events are deleted from the sample space and the remaining sample space is known as reduce sample space. Now any new event will occur from the reduce sample space instead of complete sample space. Reduce sample space simplify the problem plus it reduces the calculation work. Such kind of events whose probability is calculated from reduce sample space is known as conditional probability.