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

Here P (Not E or not F) = 0.25
$\Rightarrow P(\overline{E}\cup \overline{F})=0.25\Rightarrow \overline{(E\cap F)}=0.25\Rightarrow 1-P(E\cap F)=0.25\Rightarrow P(E\cap F)=1-0.25\Rightarrow P(E\cap F)=0.75\ne 0$
thus E and F are not mutually exclusive events.