Question: A random sample of 250 juniors majoring in psychology or communications at a large university is selected. The students are asked whether or not they are happy with their majors. The following table gives the results of the survey. Assume that none of these 250 students is majoring in two areas

                                Happy    Unhappy
Psychology                 8O            20
Communications        115           35

a. If one student is selected at random from this group. find the probability that this student is

i. happy with the choice of major
ii. a psychology major
iii. a communications major given that the student is happy with the choice of major
iv. unhappy with the choice of major given that the student is a psychology major
v. a psychology major and is happy with that major
vi. a communications major or is unhappy with his or her major

b. Arc the events -psychology major and "happy with major" independent? Are they mutually exclusive? Explain why or why not.