An urn contains 2 black and 5 brown balls. A ball is selected at random. If the ball drawn is brown, it is replaced and 2 additional brown balls are also put into the urn. If the ball drawn is black, it is not replaced in the urn and no additional balls are added. A ball is then drawn from the urn the second time.

a) What is the probability that the ball selected at the second stage is brown?

b) We are given that the ball selected at the second stage was brown. What is the probability that the ball selected at the first stage was also brown?

http://www.bilkent.edu.tr/~math250/Solution%20set2.pdf