An urn contains \(4\) white balls and \(6\) black balls. A ball is chosen at random, and its color is noted. The ball is then replaced, along with \(3\) more balls of the same color. Then another ball is drawn at random from the urn.
- Find the chance that the second ball drawn is white.
- Given the second ball drawn is white, what is the probability that the first ball drawn is black ?
- Suppose the original contents of the urn are \(w\) white and \(b\) black balls. Also after drawing a ball we replace with \(d\) balls of the same color. What is the probability that the second ball drawn is white (it should be \(\frac{w}{w+b}\) )?
[Pitman page 53. Problem 2]
