Here are the counts (in thousands) of earned degrees in the United States in a recent year, classified by level and by gender of the degree recipient:

BACHELOR MASTERS FEMALE 616 194

MALE 529 171 TOTAL 1145 365

PROFESSIONAL DOCTORATE TOTAL 30 16 856

44 26 770

74 42 1626

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

(b) What is the probability that a randomly chosen degree recipient is a man?

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

(d) What is the conditional probability that the person chosen received a bachelor's degree, given that he is a man?

(e) Are the events "choose a woman" and "choose a professional degree recipient" independent?

(f) Use the multiplication rule to find the probability of choosing a male bachelor's degree recipient.