A student takes a multiple-choice exam. Suppose for each question he either knows the answer or gambles and chooses an option at random. Further suppose that if he knows the answer, the probability of a correct answer is 1, and if he gambles this probability is 1/4. To pass, students need to answer at least 75% of the questions correctly. The student has "studied for a minimal pass," i.e., with probability 0.75 he knows the answer to a question. Given that he answers a question correctly, what is the probability that he actually knows the answer?

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