Answer
No. $P(E~and~F)\ne P(E)\times P(F)$
Work Step by Step
Suppose the events $E$ and $F$ are independent.
Using the Multiplication Rule for Independent Events (see page 282):
$P(E~and~F)=P(E)\times P(F)=0.8\times 0.5=0.4$
But, $P(E~and~F)=0.24$. So, the events $E$ and $F$ are not independent.
