A bag labeled $A$ contains $4$ red balls and $7$ green balls. Another bag $B$ contains $6$ red and $5$ green balls.
A ball is transferred from bag $A$ to bag $B$, after which a ball is drawn from $B$.
Find the probability that it is a red ball?
To be honest I have no idea how to approach the question, I assume that there would be $12$ balls in the bag $B$ when it has been transferred. I'm lost.