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Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.

16.    Events E and F are such that P(not E or not F) \small =0.25, State whether E and F are mutually exclusive. 

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Given, P(not\ E\ or\ not\ F) = 0.25

For A and B to be mutually exclusive, P(A \cap B) = 0

Now,  P(not\ E\ or\ not\ F) = P(E' \cup F') = 0.25

We know, 

P(A' \cup B') = P(A \cap B)' = 1 - P(A \cap B)
\\ \implies 0.25 = 1 - P(E \cap F) \\ \implies P(E \cap F) = 1 - 0.25 = 0.75 \neq 0

Hence, E and F are not mutually exclusive.

 

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