Two events with nonzero probabilities can be both mutually exclusive and independent cannot be both mutually exclusi…
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Question “Two events with nonzero probabilities can be both mutually exclusive and independent cannot be both mutually exclusi…”
can be both mutually exclusive and independent
cannot be both mutually exclusive and independent
are always mutually exclusive
cannot be both mutually exclusive and independent and are always
mutually exclusive
Answer
Let’s look at each answer.
“Can be mutually exclusive or independent”
This is false. These two events cannot be independent if they are mutually exclusive. Specifically, P(A|B)=0. If P(A]>0, the events are not independent.
For the above reasons, “cannot be simultaneously mutually exclusive or independent” is true.
“Are always mutually exclusive”
This is absurd.
“Cannot be mutually exclusive or independent, and must always be mutually exclusive.”
Absurd.
Let me explain what I mean by saying that events with positive probabilities cannot be said to be mutually exclusive. There is a good chance that I will attend school tomorrow. It is possible that I will have orange juice tonight. These two things are not mutually exclusive. The truth is that I can do both. The orange juice is very good.
Conclusion
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