In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $\frac{3}{5}$be the probability that he knows the answer and $\frac{2}{5}$be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $\frac{1}{3}$, what is the probability that the student knows the answer given that he answered it correctly

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