I am trying to solve this problem (no one has yet answered, though the comment by Xi'an says it is simple!)
In writing out the entropy expression, one of the probabilities is $P(X+Y|X)$. Does this expand or simplify to any other expression that could be used?
(I do not think so..., but tell me your answer)
It is not for a class. Reading a textbook (Cover Information theory), I am just stuck on this small pirnt.