Adapted from Walch Education

The conditional probability of B given A is the probability that event B occurs, given that event A has already occurred. If A and B are two events from a sample space with P(A) ≠ 0, then the conditional probability of B given A, denoted : 7.2.1: Introducing Conditional Probability2

Using set notation, conditional probability is written like this: 7.2.1: Introducing Conditional Probability3

The “conditional probability of B given A” only has meaning if event A has occurred. That is why the formula for has the requirement that P(A) ≠ 0. The conditional probability formula can be solved to obtain a formula for P(A and B) : Introducing Conditional Probability4

Independent events are two events such that the probability of both events occurring is equal to the product of the individual probabilities. Two events A and B are independent if and only if P(A and B) = P(A) P(B). The occurrence or non-occurrence of one event has no effect on the probability of the other event : Introducing Conditional Probability5

The following statements are equivalent. In other words, if any one of them is true, then the others are all true. Events A and B are independent. The occurrence of A has no effect on the probability of B; that is, The occurrence of B has no effect on the probability of A; that is, P(A and B) = P(A) P(B) : Introducing Conditional Probability6

Ms. Dambreville