Of 20 rats in a cage, 12 are males and 9 are infected with a virus that causes hemorrhagic fever. Of the 12 male rats, 7 are infected with the virus. One rat is randomly choosen from the cage.
(a) If the selected rat is found to be infected, what is the probability that it is female?
(b) If the selected rat is found to be a male, what is the probability that is infected?
(c) Are the events "the selected rat is infected" and "the selected rat is male" independent? Why or why not?