Is my answer correct? Are these two events independent? 
This is a contingency table and the question is if $D$ is independent of $A$. 
Now I know that if they are, then $P(A\cap D) = P(A)\cdot P(D)$.
So in my case, $P(A\cap D)=\dfrac{156}{810}$
$P(A)=\dfrac{234}{810}\\[3ex]$
$P(D)=\dfrac{212}{810}$
$P(A \cap D) = 0.19$
$P(A) \cdot P(D)=0.07$
So not independent. Is this correct?

Your answer is correct, assuming that A and B are mutually exclusive and exhaustive and the same for C and D.
Another way to calculate would be to see if $P(D)=P(D|A)$.
$P(D)={212\over 810}=0.262$
$P(D|A)={156\over 234}=0.667$
Since $P(D)\ne P(D|A)$, D and A are not independant.
