What does events are mutually exclusive mean?

Answer 1

Two events are mutually exclusive if the occurrence of one event implies that the other cannot occur. There is no need for either to occur.

For example, if you roll a die and the two outcomes of interest are:

A - you roll a prime

B - you roll a composite

then A and B cannot occur together. Of course, you could roll a 1, so that neither A nor B occurs.

An example of events that are not mutually exclusive is:

A - you roll a prime

C - you roll an even number

If you roll a 2 then both A and C occur.

Answer 2

It means that if one of them occurs in an experiment then the other cannot in the same experiment.