The Clemson University Fact Book for 2007 shows that 124 of the university's 309 assistant professors were women, along with 83 of the 346 associate professors and 97 of the 326 full professors.
(a) What is the probability that a randomly chosen Clemson professor is a woman?
(b) What is the conditional probability that a randomly chosen professor is a woman, given that the person chosen is a full professor?