Mutually exclusive events are events that cannot both happen at the same time:
You either like bovril or hate it.
You either do what we say or you die!
We can illustrate mutually exclusive events A and B on a Venn diagram. The sets A and B have no intersection so are mutually exclusive. We may also write
– the probability of both A and B happening is zero.
Mutually exhaustive events A and B 'cover all the possibilities'. Either A or B must happen, or both of them. The probability of neither A or B happening is zero. We may write
or
- these are just alternative notations. Events A and B may be both mutually exclusive and mutually exhaustive, in which case
If two events A and B are independent, then neither can influence the other, and we can write