## What is Conditional Probability?

If A and B are any events in S (random experiment) then the probability of occurance of event A under the condition that B has already occurred and P(B) ≠ 0, is called the conditional probability.

It is denoted by

Thus, we have = Probability of occurrence of A given that B has already occurred.

The meaning of symbols and depend on the nature of the events A and B and also the nature of the S experiment.

These 2 have following meaning:

= Probability of occurrence of A

When event B occurs or probability of occurrence of event A with respect to event B.

= Probability of occurrence of event B.

When event A occurs or probability of occurrence of event B with respect to event A.

So conditional probability of B relative to A is given by