Jane decides to challenge an AI that plays Chess. In each match, the probability that Jane wins is 2 5 . a) If Jane has 5 matches against the AI, find the probability that she wins exactly 3 matches. (4 marks) b) If Jane has 9 matches against the AI, find the probability that she wins at least 4 matches. (6 marks) c) If Jane challenges the AI until she eventually wins (once), find the probability that she takes 4 matches or more to finally win a match. (3 marks) d) If Jane has 200 matches against the AI, by using an appropriate normal approximation, estimate the probability that she wins between 76 to 92 matches (inclusive). (7 marks) [Total : 20 marks]