Academic degrees and gender. Here are the projected numbers (in thousands) of earned degrees in the United States in the 2010-2011 academic year, classi?ed by level and by the sex of the degree recipient:28

Bachelor's  Master's  Professional   Doctorate

Female          933             402                51                 26

Male              661             260                44                 26

(a) Convert this table to a table giving the probabilities for selecting a degree earned and classifying the recipient by gender and the degree by the levels given above.

(b) If you choose a degree recipient at random, what is the probability that the person you choose is a woman?

(c) What is the conditional probability that you choose a woman, given that the person chosen received a professional degree?

(d) Are the events "choose a woman" and  "choose a professional degree recipient" independent? How do you know?