In answering a question on a multiple choice questions test with four choices in each question, out of which only one is correct, a student either guesses or copies or knows the answer. The probability that he makes a guess is \frac{1}{4} and the probability the he copies is also \frac{1}{4}  The probability that the answer is correct, given that he copied it is \frac{3}{4}. Find the probability that he knows the answer to the question, given that he correctly answered it.

 

 

 

 
 
 
 
 

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