Die A has four red and two white faces, whereas die B has two red and four white faces. A coin is flipped once. If it falls heads, the game continues by throwing die A alone; if it falls tails, die B is to be used.

(a) Show that the probability of red at any throw is .

(b) If the first two throws resulted in red, what is the probability of red at the third throw?

(c) If red turns up at the first n throws, what is the probability that die A is being used?

(d) To which urn model is this game equivalent?