SUppose an urn contains $r$ red balls and $b$ blue balls. Each time a ball is drawn, it is returened along with $m$ additional balls of the same colour. Let $X_k$ be the number of red balls in $k$ draws from the urn. Find $E(X_2)$
My attempt : I think conditional expectation will be the best approach so I started with $$E(X_k) = E(E(X_k|Y))$$ where $X_k=$ # red colour in $k$ draws and $Y=1$ if at $k-1$ we get a red color and $Y=0$ if its blue. Bu I dont know how to proceed further.