When the probability of event Bis affected by the oggumrence event A the events are not independent.Let PB A) denote the probability of Bgiven the condition that Ahas occurred This is called a conditional probaality. Type by hodding down Shift and typ For independent events Aand B P(B A) =P(B), and P(A] BEPA For dependent events Aand B . PB A EP(B). The occurrence of Ahas changed the probability of B. 0 PA B #PA. The occurrence of Bhas changed the jordbabaility of A For dependent events, P(AandB) =P(A) XP(B| A) =P(B) X PA B). This is the Genera Multiplication Pue Assume the following joint and marginal probabilities In Favor Democrat Republican row total Yes 0.15 0.20 0.35 No 0.25 0.40 0.65 column total 0.40 0.60 1.0 When we know the condition that same event has occurred, the tade reduces to a rowar, column matching the condition For example, when weknowthat the party is Barrocrat, the table reduces to the Democrat column In Favor Democrat Yes 0.15 No 0.25 column total 0.40 P( Yes.| Derrocrat) is the probability of evert Yes, given the. condition that the event Democrat has occurred in condition Democrat, Yes occurs at a rate of 0.15 in 0.40. So P(Yes