In an international school, there are two foreign language courses, German and French. Each student must enroll one and only one of the two courses. According to the students' preferences survey conducted at the induction day, 60% of students decide to study German. Suppose now there are 7 students in the registration counter. (a) What is the probability that among the 7 students, all students will enroll in German course? (b) What is the probability that among the 7 students, there will be more enrolhnents in French course than German course? (0) For many groups, each with 7 students, nd the expectation and standard deviation of the number of students will enroll in German course in a group. In Alpha College, students are required to join at least one school club to get extra-curriculum activities' marks. Suppose the following table represents the probability distribution function of the number of clubs (X) a student join: x l 2 3 4 P(X = x) 0.1 2k 1: + 0.1 k (a) Find the value of k. (b) What is the probability that a student joins at most two clubs? (0) Find E(X), Var (X) and 0(X). ((1) Suppose the membership fee is $100 per club, with the rst enrolled club is free of charge. Let Y be the total membership fee a student pay. Compute E(Y) and 00'). (e) What percentage of students are paying not less than $200 for the total membership fee? (f) Write a simple paragraph (about 30 -50 words) to summarize the total membership fee a student paying for joining school club(s) (based on the results in parts (d) and (e))