In an urn there are two white balls and four black balls. A ball is drawn at random. If the ball drawn is white, it is returned to the urn and another white ball is added; if it is black, it is not returned to the urn. Next, a ball is drawn at random from the urn again.
a) (1 point) What is the probability that the two balls drawn are of different colors?
b) (1.5 points) What is the probability that the first ball drawn was black, given that the second was white?