Q. What is Conditional Probability?

Ans.

What is the probability that George will pass his math test if he studies? We can assume that the probabilities of George passing his test and George studying are dependent events. The probability of George passing his test depends on whether or not he studied for it.

Conditional probability is the probability that B will occur given that A has occurred. It is denoted by P(B | A).

The conditional probability of event B given event A, P(B | A), is given by

If events A and B are independent, then what is P(A | B)? Since the probability of event B occurring is not dependent on event A, P(A | B) = P(A). Our definition of independent events can be written more formally now.

Two events A and B are independent events if P(A | B) = P(A) or if P(B | A) = P(B).