1. Conditional Events: A and B are any two events of a finite sample space U. Under the condition ‘event A has occurred’ if event B occurs, then that event B is called the conditional event. It is denoted by the symbol B | A. Similarly, under the condition ‘event B has occurred’ if event A will occur then that event A is called the conditional event. It is denoted by the symbol A|B.
2. Law of Conditional Probability: A and B are any two events of a finite sample space U and P (A) > 0. The rule to obtain the probability of event B | A, the probability of occurrence of event B given that event A has already occurred, is called the law of conditional probability. This rule is written as under:
\(P(B|A) = \frac{P(A∩B)}{P(A)} P(A)> 0\)
Similarly, probability of conditional event A | B is obtained by following formula:
\(P(A|B) =\frac{ P(A∩B)}{P(B)}, P (B) > 0\)
