Expected value of two dependent Bernoulli random variables.

I'm in the process of finding $E(XY)$ where X and Y are non-independent Bernoulli random variables with both of them with probability of $\frac{n}{N}$

I understand that $E(XY)=\Sigma\Sigma x_{i}y_{i}P(X,Y)$ and this got me to the point where I can write:$E(XY)=P(X=1,Y=1)\cdot1+P(X=1,Y=0)\cdot0+P(X=0,Y=1)\cdot0+P(X=0,Y=0)\cdot0$$=P(X=1,Y=1)$

But Im very lost here.Some help would be appreciated.