4.6 Independent Events and Unions of Events

A and B are independent events if knowing whether or not one event has occurred doesn’t change the probability that the other event will happen. In other words, events A and B are independent if P(A | B)=P(A | BC)=P(A). Alternatively, events A and B are independent if P(B | A) = P(B | AC)=P(B). If the events are independent, then the multiplication rule becomes P(A and B) =P(A)*P(B).

The event “A or B” is known as the union of A and B, denoted by AB. It consists of all outcomes in event A, B, or both. 

The general addition rule states that if A and B are any two events resulting from some chance process, then P(A or B)=P(A)+P(B)-P(A and B).