Solution
= Solution
The sole green ball comes from the first bag exactly on the event $(X,Y)=(1,0)$. Divide this joint <probability> by the conditioning event's <probability>:
$$
\boxed{P(X=1,Y=0\mid X+Y=1)
=\frac{(3/5)(2/3)}{13/30}=\frac{12}{13}}.
$$
This is the <conditional probability> form of <Bayes' theorem>.