Having endured and survived the mental trauma that comes from taking two years of chemistry, a year of physics, and a year of biology, Bill decides to test the medical school waters and sends his applications to two colleges X and Y. Based on how his friends have fared, he estimates that his probability of being accepted at X is 0.7, and at Y is 0.4. He also suspects that there is a 75% chance at least one of his applications will be rejected. What is the probability that Bill was accepted at College Y given that he was accepted at College X?

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