Let X1 and X2 be the numbers on two independent fair-die rolls. Let X be the minimum and Y the maximum of X1 and X2. Calculate: $E(Y|X=x)\qquad\text{and}\qquad E(X|Y=y) $ given that X1 and X2 independent and uniformly distributed on $\{1,\ldots,n\}$.
What I was able to do was trying to rewrite $E(Y|X=x) = E(Y,X=x)/(E(X=x))$, but this does not seem to helpful. Also, what can I do with the fact that they are indpendent and uniformly distributed?