Do mutually exclusive events simply refer to dependent events? To add to the confusion, I also learned that mutually exclusive events can be independent event in a special case when probability is zero i.e. P(A)=0 or P(B)=0. But an event should either be independent or dependent and not both?

sublimnes9

sublimnes9

Open question

2022-08-15

Do mutually exclusive events simply refer to dependent events?
To add to the confusion, I also learned that mutually exclusive events can be independent event in a special case when probability is zero i.e. P ( A ) = 0 or P ( B ) = 0 .
But an event should either be independent or dependent and not both?

Answer & Explanation

Lisa Acevedo

Lisa Acevedo

Beginner2022-08-16Added 18 answers

By definition, two events A and B are mutually exclusive whenever A B = . In that case, one has P ( A B ) = 0. Some people also say that A and B are mutually exclusive whenever P ( A B ) = 0. (The second condition is weaker, but it doesn't make a difference in practice.)
Now, two events A and B are called independent, if P ( A B ) = P ( A ) P ( B ).
Can you now see in which cases you have that A and B are mutually exclusive and independent?

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