What is the difference between events that are mutually exclusive and those that are not mutually exclusive?
Any event can be viewed as a combination of certain elementary events. Thus, an event of rolling a dice on an even number is, actually, a set of three elementary events - rolling numbers 2, 4 and 6.
Now, if two events are considered, each representing a subset of a set of all possible elementary events, they might or might not have certain number of elementary events in common. If they don't, these two events are called mutually exclusive. If they do, they are not mutually exclusive.
An example of mutually exclusive events are
Obviously, there is no elementary event that simultaneously belongs to events
An example of not mutually exclusive events are
Obviously, the elementary events