Chapter 6, Problem 6P

Second Paradox: The probability of a male applicant being admitted to a graduate school can be higher than the probability for a female applicant, even though for each department the probability of a female being admitted is higher. (This apparent contradiction is known as Simpson’s paradox.)

To simplify matters, consider a university with two professional graduate programs, medicine and law. Suppose that last year 1000 men and 1000 women applied, and the outcome was as shown in Table 1.

Table 1
	Men			Women
	Applied	Accepted	Rejected	Applied	Accepted	Rejected
Law Medicine	700 300	560 40	140 260	400 600	340 160	60 440

What is the probability that a male applicant was accepted to a professional program? A female applicant?