Conditional probability

Conditional probability:

Let A be any event with p(A) >0. The probability that an event B occurs subject to the condition that A has already occurred is known as the conditional probability of occurrence of the event B on the assumption that the event A has already occurred and is denoted by the symbol P(B/A) or P(B|A) and is read as the probability of B given A.

The same definition can be given as follows also:

Two events A and B are said to be dependent when A can occur only when B is known to have occurred (or vice versa). The probability attached to such an event is called the conditional probability and is denoted by P(B/A) or, in other words, probability of B given that A has occurred.

If two events A and B are dependent, then the conditional probability of B given A is

P(B / A) = P(A Ç B)

P(A)

Similarly the conditional probability of A given B is given as

P(A / B) = P(A Ç B) / P (B)

If the events A and B are independent, that is the probability of occurrence of any one

of them P(A/B) = P(A) and P(B/A) = P(B)