2.6 Conditional Probability

Calculate conditional probabilities.

• The probability that event A will occur given that event B has occurred is called a conditional probability and is written as P(|AB ). Conditional probability is defined as P AB PB PB(| ) = ∩() () A .
• The general multiplication rule states that the probability that events A and B both will occur is equal to the probability that event A will occur multiplied by the conditional probability that event B will occur given that event A has occurred. The multiplication rule is defined as P AB PP BAA∩() = () . (| ) .