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#1




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? 
#2




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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exam p, independence, mutually exclusive, probablity 
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