Question 11 {13 marks} A four-sided die has three green faces and one pink face. The die is rolled. Let G be the event a green face lands down, and P be the event a pink face land down. a} (2 marks} Write down P(G) and P(P) b} (2 marks} If the green face lands down, the die is not rolled again. if the pink face lands down, the die is rolled again. Represent this information with a tree diagram, indicating the probabilities of each branch. Guilia plays a game where she rolls the die. If a green face lands down, she scores two points and is nished. lfa pink face lands down, she scores 1 point and rolls one more time. Let X be the total score obtained. c} (2 marks} Find P(X = 3) d} (2 marks} Find P(X = 2) e} (1 mark} Construct a probability distribution of X. f) (2 marks} Calculate the expected value ofX. g} (2 marks} Ifthe total score is 3, Guilia wins $10. If the total score is 2, she gets nothing. Guilia plays the game twice. Find the probability that she wins exactly 510