[Maximum mark: 6] A 6 sided die has 3 sides that are white, two sides that are blue, and one side that is red. Lily rolls this die twice and records the colors of the upward side both times. The following tree diagram shows all the possible outcomes of these two rolls. 1/6 red red 1/3 blue 1/2 1/6 white 1/6 red 1/3 blue 1/3 blue 1/2 white 1/2 1/6 red white 1/3 blue 1/2 white (a) Find the probability that both die rolls show red. 1/36 [2] (b) Find the probability that at least one of the die rolls show white. 1/12 [2] (c) Find the probability that the second roll shows red, given that the first roll showed blue. [2] 1/18