Suppose you have three events - X, Y, and Z - where X and Y are mutually exclusive, and together X, Y, and Z are collectively exhaustive. Z is not mutually exclusive with respect to either X or Y. Is this possible? If so, draw a Venn Diagram illustrating how it might be possible.

Answer:

X and Y are mutually exclusive events that is both cannot occur together means there in nothing common between two of them.

X,Y and Z are collectively exhaustive that is atleast one of the event must occur.

Z is not mutually exclusive with either X or Y that is there is some common part between X,Z and Y,Z .

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