Question

The compound probability of two events, E and F 1/8 , is ; the probability of E is 1/2 and of F is 1/3 . In two or more complete sentences, explain why E and F are not independent.

Answer 1

If they are independent then it should hold true that P(A) X P(B) = P(A and B)
This is not the case for F and E in the questions so therefore they are independent.

Answer 2

Answer:

Event E and event F are not independent because:

        $P(E\bigcap F)\neq P(E)\times P(F)$

Step-by-step explanation:

We know that two event A and event B are said to be independent if:

         P(A∩B)=P(A)×P(B)

Here we have two events as E and F such that:

$P(E\bigcap F)=\dfrac{1}{8}$

$P(E)=\dfrac{1}{2}$

and $P(F)=\dfrac{1}{3}$

This means that:

$P(E)\times P(F)=\dfrac{1}{2}\times \dfrac{1}{3}\\\\\\i.e.\\\\\\P(E)\times P(F)=\dfrac{1}{6}\neq P(E\bigcap F)$

        Hence, the events E and F are not independent.