4. (4 points) A high school with 1000 students offers two AP courses: Statistics and Calculus. There are 200 students in the Calculus class roster, and 180 students in the Statistics class roster. We also know that 100 students enroll in both courses.

(a) (2 points) Find the probability that a randomly selected student takes neither AP course. (Show work and write the answer in simplest fraction form)

(b) (2 points) Let event A be that a randomly selected student takes AP Statistics course, and event B be that a randomly selected student takes AP Calculus course. Are A and B independent? Use mathematical expression to justify your answer.

5. (2 points) The steering committee of UMUC Green Solutions Team consists of 3 people. 10 members are interested in serving in the committee. How many different ways can the committee be selected? (Show work)