Problem 2. [20 pts] I have three urns U1 U2 and U3 such the first urn contains wi ?dentical white balls and b. identical black balls, the second urn contains w2 identical white balls and b2 identical black balls, and the third urn contains ws identical white balls and ba identical black balls. I first choose a ball uniformly at random from U, (i.e., every ball is equally likely to be picked) and drop it into U2. Next, I pick a ball uniformly at random from U2 and drop it into Us Finally, I pick a ball uniformly at random from Us and it turns out to be white. What is the probability that the ball that was transferred from Ui to U2 was black? Show the main steps of your solution. Hint: Note that this problem is asking for a conditional probability. Use the tree method