Question 5 [20 points) According to the record of the registrar's ofce at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20%. (l What is the probability that a randomly selected student is a freshman and shefhe lives in a dormitory? (2 points} 'What is the probability that a randomly selected student is a sophomore and shejhe does not live in a dormitory? (2 points} What is the probability that a randomly selected student is a junior or senior and shefhe lives in a dormitory? (2 points} What percentage of the students live in a dormitory? (2 points) 'What percentage of the students do not live in a dormitory? (2 points] If a randomly selected student lives in the dormitory, what is the probability that the student is a freshman? (2 points} If a randomly selected student lives in the dormitory, what is the probability that the student is ajunior or a senior? Please apply the Bayes' Rule to calculate the probability. (4 points} (8) Construct a frequency contingency table to verify your above answers. (4 points}