Question

The compound probability of two events E and F is 1/8; the probability of E is 1/2 and of F is 1/3. E and F are independent.

Answer 1

If E and F were independent, the product of their probabilities would be:
$\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$
Therefore the statement in the question is FALSE.

Answer 2

The events, E and F, are independent if we get the value of their compound probability when we multiply the probability of E and probability of F. 
                   compound probability ____ P (E) x P (F)
                         1/8 ____ (1/2) x (1/3) = 1/6
Since the probabilities are not equal, the events are DEPENDENT. Therefore, the answer is FALSE.