Question

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

Answer 1

It is given that P (not E or not F) = 0.25
i.e, P(E'UF') = 0.25
$⇒$P(E∩F)'=0.25

Now, P(E∩F) =1-P(E∩F)'
$⇒$ P(E∩F) =1-0.25
$⇒$ P(E∩F) =0.75≠0
$⇒$ E∩F$≠\phi$
Thus, E and F are not mutually exclusive.