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Old 08-07-2019, 12:00 PM
adamrandall21 adamrandall21 is offline
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Default Independence / Mutually Exclusive Events

While studying general probability for Exam P, Coaching Actuaries says that two events cannot be both independent and mutually exclusive. Why is this?

I know that independent events means that event A occurring does not influence the likelihood that event B occurs. I know that events A and B are mutually exclusive if the probability of their intersection is zero.

One thought I have is that two events are independent if and only if pr(A∩B) = Pr(A)*Pr(B). However, if A and B are mutually exclusive events, then pr(A∩B)=0. Is this why they cannot be both independent and mutually exclusive?
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Old 08-07-2019, 01:11 PM
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Vorian Atreides Vorian Atreides is offline
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Consider the (non-trivial) situation where Both P(A) and P(B) are greater than zero. (That is, neither A nor B are impossible).

Definition of independence is that P(A & B) = P(A)*P(B) > 0.

Mutually Exclusive requires that P(A & B) = 0.

Yes, what you said is correct.
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Old 08-12-2019, 08:33 PM
Berkmaster Berkmaster is offline
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If they are mutually exclusive, then one occurring means the other cannot. Intuitively, this means they have some connection. How could they then be independent?
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Old 08-12-2019, 08:36 PM
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campbell campbell is offline
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Well, they can be.

If P(A) = P(B) = 0

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exam p, independence, mutually exclusive, probablity

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