Bag A contains 3 black marbles and 1 white marble and Bag B contains 1 black marble and 3 white marbles. If two marbles are randomly taken from Bag A and placed in Bag B, then a marble is randomly selected from Bag B, what is the probability that the marble selected from Bag B is black?

I've tried to draw a tree, but I must be doing something wrong cause I can't get the correct answer. Could someone give me some guidance?