Three Bags, A, B and C, each contain 1 red marble and some green marbles.

Bag A contains 1 red marble and 9 green marbles only

Bag B contains 1 red marble and 4 green marbles only

Bag C contains 1 red marble and 2 green marbles only

Sasha selects at random one marble from Bag A. If he selects a red marble, he stops selecting. If the marble is green, he continues by selecting at random one marble from Bag B. If he selects a red marble, he stops selecting. If the marble is green, he continues by selecting at random one marble from Bag C.

(a) Draw a tree diagram to represent this information.

(b) Find the probability that Sasha selects 3 green marbles.

(c) Find the probability that Sasha selects at least 1 marble of each colour.

(d) Given that Sasha selects a red marble, find the probability that he selects it from Bag B.