Let A and B be independent events. Let C = A B. Conditional on C, are A and B independent? Use the following hypothetical scenario to answer this question: Suppose that in the population of college applicants, academic ability and athletic ability are independent. Additionally, suppose that a college admits applicants entirely based on academic ability and athletic ability: applicants are admitted if their academic ability is rated in the 95th percentile or their athletic ability is rated in the 95th percentile. Demonstrate numerically whether academic ability and athletic ability are independent among the admitted applicants. Explain your reasoning.