This is our definition of conditional probability: Definition:Let 4 and B be two events with P(B)>0.The conditional probability that event 4 occurs,given that event B has occurred,is written P(A B),and is given by P(A|B)= P(A0B) P(B) Read P(A B)as "probability of A,given B". Note:P(A B)gives P(A and B,from within the set of B's only). P(AnB)gives P(A and B,from the whole sample space Note:Follow the reasoning above carefully.It is important to understand why the conditional probability is the probability of the intersection within the new sample space Conditioning on event B means changing the sample space to 中 Think of P(A B)as the chance of getting an A,from the set of B's only. The Multiplication Rule For any events A and B, P(AB)=P(A B)P(B)=P(B A)P(A). This is our definition of conditional probability: Definition: Let A and B be two events with P(B)>0. The conditional probability that event A occurs, given that event B has occurred, is written P(A|B), and is given by Note: Follow the reasoning above carefully. It is important to understand why the conditional probability is the probability of the intersection within the new sample space Conditioning on event B means changing the sample space to B. Think of P(A|B) as the chance of getting an A, from the set of B's only. The Multiplication Rule For any events A and B