With respect to a particular question on a multiple choice test (having 4 alternatives with only...

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With respect to a particular question on a multiple choice test (having 4 alternatives with only 1 correct) a student knows the answer and therefore can aliminate 3 of the 4 choices from consideration with probability \( 2 / 3 \), can eliminate 2 of the 4 choices from consideration with probability \( 1 / 6 \), can elimiate 1 choice from consideration with probability \( 1 / 9 \), and can eliminate none with probability \( 1 / 18 \). If the student knows the answer, he answers correctly, otherwise he guesses from among the choices not eliminated.

If the answer given by the student was found correct, then the probability that he knew the answer is \( a / b \) where \( a \) and \( b \) are relatively prime. Find the value of \( (a+b) \).
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