In answering a question on a multiple choice test a student either knows the answer or guesses. ...

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In answering a question on a multiple choice test a student either knows the answer or guesses. Let \( 3 / 4 \) be the probability that he knows the answer and \( 1 / 4 \) be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability \( 1 / 4 \). What is the probability that a student knows the answer given that he answered it correctly?
(a) \( \frac{5}{17} \)
(b) \( \frac{12}{13} \)
(c) \( \frac{17}{30} \)
(d) \( \frac{3}{5} \)
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