Polya’s urn scheme. An urn contains 4 red and 6 green balls. One ball is drawn at random and its color is observed. The ball is then returned to the urn, and 3 new balls of the same color are added to the urn. A second ball is then randomly drawn from the urn that now contains 13 balls.

(a) List all outcomes of this experiment (use symbols such as R1G2 to denote the outcome of the first ball red and the second green).

(b) What is the probability that the first ball drawn is green?

(c) What is the conditional probability of getting a red ball in the second draw given that a green ball appears in the first?

(d) What is the (unconditional) probability of getting a green ball in the second draw?