Women in math (5.3) Of the 24,611 degrees in mathematics given by U.S. colleges and universities in a recent year, 70% were bachelor’s degrees, 24% were master’s degrees, and the rest were doctorates. Moreover, women earned 43% of the bachelor’s degrees, 41% of the master’s degrees, and 29% of the doctorates.7

(a) How many of the mathematics degrees given in this year were earned by women? Justify your answer.

(b) Are the events “degree earned by a woman” and

“degree was a bachelor’s degree” independent?

Justify your answer using appropriate probabilities.

(c) If you choose 2 of the 24,611 mathematics degrees at random, what is the probability that at least 1 of the 2 degrees was earned by a woman? Show your work.