Suppose 90 men are admitted and 10 men are denied to the math department, and 1 man is admitted while 9 men are denied to the English department, at 2DU (Two Department University). Suppose the corresponding numbers for women are: 9, 1, 10, 90. a. Show that gender and admission rate at 2DU are not independent, but that they are conditionally independent when you condition on the department. b. What are the prior odds that a random applicant is a man