Thanks, that is a good observation. So now I know that
P(X>a,X>Y) = P(X>max(a,Y)). I would like to express this as some function of P(X>a) and P(X>Y) . That is, I know that
P(X>a,X>Y) = [ P(X>a) if a>Y
[ P(X>Y) if a<Y
but I only know a, not Y (since Y is an RV)...