Question 3 In the video game Super Italian Plumber Party, each player chooses a character and on their turn, they roll a 9-sided die corresponding to their character. After rolling the die, they move forward a number of spaces based on the number which was rolled. Super Italian Plumber Party has four different characters who each have a unique 9-sided die. These die are all fair; that is, on each of the dice in Super Italian Plumber Party the probability of any face being rolled is and all rolls are independent of one another. The table below shows the sides of the dice for each of the characters. Character Side 1 Side 2 Side 3 Side 4 Side 5 Side 6 Side 7 Side 8 Side 9 Dario Giulio 1 2 3 4 5 6 7 8 9 0 0 0 0 9 9 9 9 9 Princess Pear 2 4 4 4 6 6 6 6 8 Trouser -2 -2 -2 3 3 9 9 14 14 a) What is the expected value and variance of each of the four dice in Super Italian Plumber Party? (4 marks) b) In order to win Super Italian Plumber Party, your character must reach the finish line before the end of the game. Suppose that the game is going to end in two turns and every character is exactly 13 spaces away from the finish line. What is the probability of each character reaching the final square before the end of the game? (6 marks)