Exams Are Difficult!

In a test, an examine either guesses or copies or knows the answer to a multiple choice question with four choices. The Probability that he makes a guess is \(\dfrac{1}{3}\) and the probability that he copies the answer is \(\dfrac{1}{6}.\) The probability that his answer is correct, given that he copied it, is \(\dfrac{1}{8}\). Find the probability that he knew the answer to the question, given that he correctly answered it.

  • If the probability can be written as \(\dfrac{a}{b} \), where \(a\) and \(b\) are coprime positive integers,
  • Find \(a\times b\).
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