Sunday, June 25, 2006
Mutually exclusive vs. independent
Some people confuse the probabilistic concepts of mutually exclusive events and independent events, but the two are not the same. In fact, independent events with positive probability cannot be mutually exclusive:
P(A)>0, P(B)>0 => P(AB) = P(A)*P(B) >0 but P(AB) = 0 for mutually exclusive events.
[Here P(AB) = probability of the intersection of A and B; for independent events, P(AB)=P(A)*P(B).]
Heuristically, if you have two events that are mutually exclusive, then knowing one occurred means that you automatically know the other did not occur. Since independent events do not affect each other, that means they cannot be mutually exclusive.