Did he know the answer?

In answering a question on MCQ test with 4 choices per question, a student either knows the answer or guesses or copies the answer. Let \(\cfrac { 1 }{ 2 } \) be the probability that he knows the answer, \(\cfrac { 1 }{ 4 } \) be the probability that he guesses and \(\cfrac { 1 }{ 4 } \) be the probability that he copies it.

Assuming that a student who copies the answer has a \(\cfrac { 3 }{ 4 } \) probability to be right, what is the probability that the student knows the answer, given that he answered it correctly? Give your answer to 3 decimal places.

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