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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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