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2. (10 points) Minwoo Park received a letter from 'Military Manpower Administration' in Korea and got draft notice. Minwoo was crying but he noticed that he had to choose a branch to join. He really wanted to stay near his hometown. He had three options to join: Republic of Korean Army (ROK), Republic of Korean Airforce (ROKAF), and Korean Augmentation To the United States Army (KATUSA). Considering all factors that affect his decision, the probabilities of choosing these branches are 0.2 for ROK, 0.5 for ROKAF, and 0.3 for KATUSA, respectively. Suppose that the probabilities of working near his hometown are 0.05 given that Minwoo goes to ROK, 0.35 given that he goes to ROKAF, and 0.6 given that he goes to KATUSA, respectively. (Simplify your results to one irreducible fraction when your answer is a fraction.) (a) What is the probability that Minwoo can't work near his hometown. (b) What is the probability that Minwoo joined ROKAF, given that he worked near his home- town. (c) What is the probability that Minwoo didn't join ROK, given that he couldn't work near his hometown. (d) Are events that Minwoo joins ROKAF and that Minwoo work near hometown indepen