Anne plays a game in which a fair six-sided die is thrown once. If the score is 1, 2 or 3, Anne loses 10. If the score is 4 or 5, Anne wins fx. If the score is 6, Anne wins 2x.

(a) Show that the expectation of Anne's profit is (x-5) in a single game.

(b) Calculate the value of x for which, on average, Anne's profit is zero.

(c) Given that x-12, calculate the variance of Anne's profit in a single game. (C)