Conditional Probability: In some situations, the chance of occurrence of a particular event depends on some other event. The multiplication law explained above is not applicable in case of dependent events. For example, the chance that a patient with some disease survives the next year depends, of course, on his having survived to the present time and the current status of his disease. Such probability is called Conditional Probability.
Definition
The probability of the simultaneous occurrence of two events A and b is equal to the probability of A multiplied by the conditional probability of B, given that A has occurred (or it is equal to the probability of B multiplied by the conditional probability of A given that B has occurred). In symbols,
P (AB) = P(A).P (B│A)
= P(B).P (A│B)
