Question 5 In a game of mini roulette, the dealer spins a ball around a wheel which has eight slots numbered from 1 to 8. The ball has an equal chance of landing in any of the eight slots. If the dealer spins the wheel four times in a row, find the probability that: a) The ball lands in slot 7 each time. Give your answer as an exact fraction or to 3 significant figures. (2 marks) b) The ball lands in slot 5 at least once. c) The ball lands exactly three times in slot 2 (4 marks) (4 marks) The mini roulette is now played with an unfair wheel which is represented by a discrete random variable X which has the probability density function p(x) = P(X = x) shown in the following table: 1 2 3 4 5 6 7 8 0.1 0.05 0.05 0.12 0.03 p(x) 0.2 c) If p(2) = 3 p(4), calculate p(2) and p(4). d) Calculate E(X). e) Calculate Var(X). (3 marks) (3 marks) (4 marks)