Can you figure out this apparent paradox?

There was a mathematically interesting lawsuit against the University of California Berkeley graduate school claiming that men were consistently accepted at a higher rate than women. The university looked at the acceptance rates for each department and found that at the department level women were accepted at a slightly higher rate than men. How is this possible? To simplify things suppose there are just two departments with equal numbers of total applicants. Can you come up with numbers that have women at each department being accepted at a higher rate than men but overall men are accepted at a higher rate?

This is an example of what is referred to as Simpson’s paradox. It is not really a paradox and requires no advanced math to see how it can happen.