An urn contains 4 white and 6 black marbles. A first marble is chosen at random and its color noted. The marble is then replaced (i.e. put back in the urn) along with 3 more marbles of the same color . Finally, a second marble is drawn at random from the urn. (a) Find the probability that the second marble is white. (b) Given that the second marble is white, what is the probability that the first marble was white? (c) Let's take this a step further. Suppose that the original contents of the urn are: w white marbles and b black marbles. After a marble is drawn from the urn, it is replaced (put back in the urn) with m more marbles of the same color . Finally, a second marble is drawn from the urn. What is the probability that the second marble is white? Hint: Interestingly, you will find that the answer does not depend on m.