Let random variables X,Y independent Bernoulli random variables, $Z=X+Y$
I need to calculate the I (X:Y|X+Y)
So obviously, I get :
\begin{eqnarray*} I(X;Y|Z)&=&H(X|Z)-H(X|Y,Z) \end{eqnarray*}
also we know that $H(X|Y) = H(X)$ because they are independent. The thing is here i am stuck. can i get an explanation please? Thanks!