So, two events are mutually exclusive if they have an empty set, and two events are independent if they do not affect each other.

However, is it possible for two events to be mutually exclusive but not independent?

For example, the p(A) = {card < 5 is drawn} and p(B) = {face card is drawn}.

p(A&B) = 0, p(A) = 12/52, p(B) = 12/52

Test for independence fails since p(A&B) does not equal p(A)*p(B). Therefore, this must mean that the events are not independent but are mutually exclusive.

Is this logically possible?