There are 200 students in a particular graduate program at a state university. Of them, 110 are female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students.
a. Are the events “female” and “out-of-state student” independent? Are they mutually exclusive? Explain why or why not.
b. If one of these 200 students is selected at random, what is the probability that the student selected is
i. A male?
ii. An out-of-state student given that this student is a female?