Assume that, among faculty who teach at community colleges, 30% hold doctoral degrees, 60% are female, and 12% are female and hold doctoral degrees.
(a) If two community college faculty members are independently chosen at random, determine the probability that neither of them will hold doctoral degrees?
(b) If one community college faculty member is chosen at random, determine the probability that the chosen person will be female or hold a doctoral degree (or both)?
For community college faculty, are the events "is female" and "holds a doctoral degree" independent? Why or why not?