Question: When the probability of event B is affected by the occurrence of event A, the events are not independent. Let P(B | A) denote the probability of B given the condition that A has occurred. This is called a conditional probability.

When the probability of event B is affected by the occurrence of event A, the events are not independent. Let P(B | A) denote the probability of B given the condition that A has occurred. This is called a conditional probability. Type | by holding down Shift and type For independent events A and B, P(B | A) P(B), and P(A | B) P(A) For dependent events A and B P(B A) P(A B) = P(B). The occurrence of A has changed the probability of B P(A). The occurrence of B has changed the probability of A For dependent events, P(A and B) General Multiplication Rule. P(A) x P(B A)= P(B) x P(A| B). This is the Assume the following joint and marginal probabilities: row In Favor Democrat Republican 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 some event has occurred, the table reduces to a row or column matching the condition. For example, when we know that the party is Democrat, the table reduces to the Democrat column: In Favor Democrat Yes 0.15 No 0.25 column total 0.40 P(Yes | Democrat) is the probability of event 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 | Democrat) = 0.15/0.40 = 0.375 P(Male | Republican) is a probability. Conditional Joint