# If events are mutually exclusive are they independent?

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soq Share
Feb 9, 2018

For mutually exclusive events, $P \left(A \setminus \cap B\right) = 0$

For independence, $P \left(A \setminus \cap B\right) = P \left(A\right) \cdot P \left(B\right)$

If two mutually exclusive events are independent then $P \left(A \setminus \cap B\right) = 0 = P \left(A\right) \cdot P \left(B\right)$

$\implies P \left(A\right) = 0$ or $P \left(B\right) = 0$

So, either of those events is impossible. Two positive mutually exclusive events cannot be independent.

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