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

P(E)≤P(F)P(E)≤P(F)

P(E∩F)>0P(E∩F)>0

Since P(E∩F)>0, P(E) not equals to P(F) so occurrence of

E is not same as F

Also,1-P(E) not equals to 1-P(F) so non-occurrence of E is also

not equals to non- occurrence or occurrence of F

P(E∩F)>0