# 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)*P(D)

Is my answer correct? Are these two events independent?
$\begin{array}{|ccc|}\hline & A& B\\ C& 78& 520\\ D& 156& 56\\ \hline\end{array}$
This is a contingency table and the question is if D is independent of A.
Now I know that if they are, then $P\left(A\cap D\right)=P\left(A\right)\cdot P\left(D\right)$
So in my case, $P\left(A\cap D\right)=\frac{156}{810}$
$P\left(A\right)=\frac{234}{810}\phantom{\rule[-3ex]{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$
$P\left(D\right)=\frac{212}{810}$
$P\left(A\cap D\right)=0.19$
$P\left(A\right)\cdot P\left(D\right)=0.07$
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bibliothecaqz
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 $P\left(D\right)=P\left(D|A\right)$
$P\left(D\right)=\frac{212}{810}=0.262$
$P\left(D|A\right)=\frac{156}{234}=0.667$
Since $P\left(D\right)\ne P\left(D|A\right)$, D and A are not independant.