If A and B are two envents associated with a random experiment, then the probability of occurence of the event A under the condition that B has occurred and P(B)≠0

Thus P(A/B)=probability of occurence of event A given that event B has already occured and P(B)≠0

Let S be the sample space having ‘n’ equal likely outcomes of a random experiment. Let A and B be two events of sample space S.

a is number of outcomes in A

b is number of outcomes in B

t is number of outcomes in A∩B

Then

Note: The outcomes of B which are favourable to A are the common outcomes of A and B that is, outcomes of A&capB

provided P(B)≠0

orprovided P(B)≠0

Similarlyprovided P(A)≠0

### Properties of Conditional Probability

The conditional probability of an event A given that B has occurred lies between 0 and 1

If A and B are two events associated with a random experiment having sample space S and if F
is an event such that P(F)≠0, then

and if A and B are disjoint sets