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.

a. How many of the mathematics degrees given that year were earned by women? Justify your answer.

b. Suppose we randomly select a person who earned a mathematics degree in this recent year. 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.