# Is it possible for events A and B to be both mutually exclusive and independent? Justify your answer.

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Is it possible for events A and B to be both mutually exclusive and independent? Justify your answer.

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Step 1

Disjoint Events:  Two events A and B are disjoint or mutually exclusive if and only if both do not occur at the same time. So, we can say that the probability of both events occuring together P(A ∩ B) = 0.

Independent Events: Two events A and B are independent events if and only if the occurrence of one event does not affect the occurrence of the other event. So, If any two events are independent the P(A ∩ B) = P(A)*P(B)

Step 2

Given that two events If A and B are disjoint then they are independent. If A and B are disjoint then both events A and B do not occur at the same time. So we can say P(A∩B) =0. If event A occur then B do not occur and if event B occur then event  A do not occur.

If two events are independent then P(A∩B)=P(A)P(B). Let us assume events A and B are disjoint andind...

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