Mutually Exclusive Events

Two events are mutually exclusive or disjoint when the occurrence of one event prevents the other. That is, their joint probability . An example of mutually exclusive event is getting a sum of 12 from 2 dice throws and throwing a 1.

If two events are mutually exclusive, we can add their probability:

This is obviously not correct in general when the two events are not mutually exclusive.

Relationship with Independence

Note that mutually exclusive events are neither necessarily independent or dependent. In any non-trivial case, mutually exclusive events are dependent. However, it is possible for two mutually exclusive events to be independent when one event is impossible to happen.