One bag contains 6 white and 4 black balls, and a second bag contains 3 white and 7 black balls. One ball is drawn at random from the first bag and placed unseen in the second bag.
(a) Find the probability that a ball now drawn at random from the second bag will be black.
(b) If the ball drawn from the second bag is black, find the probability that a black ball was transferred from the first bag.
I drew a tree diagram for both of them but the fact that the balls get switched into another bag confuses me : / need some help