Mutually Exclusive, Independent and Exhaustive Events Illustrated on Venn Diagrams

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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! (George Bush’s sentiment).

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 writeor– 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

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