A company offers a basic life insurance policy to its employees, as well as a supplemental life insurance policy. To purchase the supplemental policy, an employee must first purchase the basic policy. Let X denote the proportion of employees who purchase the basic policy, and Y the proportion of employees who purchase the supplemental policy. Let X and Y have the joint density function f(x, y) = 2(x + y) in the region where the density is positive. Find the probability that more than twice as many employees buy the basic policy as the supplemental policy.