# 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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