Question 3 (a) (b) In a 3-game series, two teams (Jurong and Tampines) will play until one team wins 2 games. Even though the two teams are equally competent, since there i1s a \"home game advantage\". a team who plays in their home stadium will win with probability P, where P > 0.5, Consider the case where Team Tampines will start their season by starting in Tampines Stadium (1.e. they will win the first game with probability P). Subsequently., the second round will take place at Jurong Stadium, and if required. the third round will return to Tampines Stadium. (1) By drawing a tree diagram or otherwise. determine all possible outcomes from this season and their associated probabilities. (10 marks) (1) Create the PMF for T. the number of individual games won by Tampines team. (5 marks) A hospital offers two types of cancer screenings: Screeming A and Screening B. Research indicates that 1% of the population has cancer. Screening A correctly identifies cancer in 95% of cases and gives a false positive 1 3% of cases. Screening B correctly identifies cancer in 90% of cases and gives a false positive in 2% of cases. If a patient tests positive for cancer using either screening method. what 1s the probability that they actually have cancer? Calculate this using Bayes' Theorem. (6 marks for each sereening) Also. comment on your results. Which test would you take?