In a fairground game a competitor scores 0, 1, 2 or 3 with probabilities given in the following table, where a and b are constants. Score 0 2 3 Probability a b b b The competitor's expected score is 0.9. (a) Show that b = 0.15. [2] (b) Find the variance of the score. [3] (c) The competitor has to pay $2.50 to take part, and wins a prize of f2.), where X is the score achieved. Find the expectation of the competitor's loss. [2]