In a large corporation, 80% of the employees are men and 20% are women. The highest levels of education obtained by the employees are graduate training for 10% of the men, undergraduate training for 30% of the men, and high school training for 60% of the men. The highest levels of education obtained are also graduate training for 15% of the women, undergraduate training for 40% of the women, and high school training for 45% of the women.

a. What is the probability that a randomly chosen employee will be a man with only a high school education?

b. What is the probability that a randomly chosen employee will have graduate training?

c. What is the probability that a randomly chosen employee who has graduate training is a man?

d. Are gender and level of education of employees in this corporation statistically independent?

e. What is the probability that a randomly chosen employee who has not had graduate training is a woman?