Question

If E and F are event with $P\left(E\right)\le P\left(F\right)$ and $P(E\cap F)>0,$ then

• A. Occurrence of E Occurrence of F
• B. Occurrence of F Occurrence of E
• C. Non-occurrence of E Non-occurrence of F
• D. None of the above implications holds

Answer 1

The correct option is D None of the above implications holds

$P\left(E\right)\le P\left(F\right)\Rightarrow n\left(E\right)\le n\left(F\right)$
$P(E\cap F)>0\Rightarrow E\cap F\ne \Phi$
These do not mean that E is a sub-set of F and F is a sub-set of E. i.e, $E\subseteq ForF\subseteq Eor\overline{E}\subseteq \overline{F}$