Definition:Disjoint Events

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Definition

Let $A$ and $B$ be events in a probability space.

Then $A$ and $B$ are disjoint if and only if:

$A \cap B = \O$


It follows by definition of probability measure that $A$ and $B$ are disjoint if and only if:

$\map \Pr {A \cap B} = 0$


That is, two events are disjoint if and only if the probability of them both occurring in the same experiment is zero.

That is, if and only if $A$ and $B$ can't happen together.


Also known as

$A$ and $B$ are also referred to in this context as mutually exclusive.


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