Question

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

• A. occurrence of E $\Rightarrow$ occurrence of F
• B. occurrence of F$\Rightarrow$ occurrence of E
• C. non occurrence of E $\Rightarrow$ non occurrence of F
• D. none of the above implications holds

Answer 1

The correct option is D none of the above implications holds

Given,$P\left(E\right)\le P\left(F\right)andP(E\cap F)>0$
$\Rightarrow$ there is a some common exist between E and F which is shown in below image.
1) Occurence of E doesn't always $\Rightarrow$ occurence of F,since $E\ne F$ always.when E<F,There is chance of occuring E irrespective of occurence of F
2)Similary Occurence of F doesn't always $\Rightarrow$ occurence of E,since $E\ne F$.when E<F,There is chance of occuring F irrespective of occurence of E
3)Similary Occurence of E doesn't always $\Rightarrow$ non-occurence of F,since $E\ne F$.There might be a chance of F to occur irrespective of E not occuring.
$\therefore$ None of the given options are correct.