A probability problem by Akshit Kumar

Probability Level 3

In an entrance test there are multiple choice questions. There are four possible answers to each question of which exactly one option is correct. The probability that a student knows the answer to a question is 90 %. If he does not know the answer, he guesses randomly. Given that he gets the correct answer to a question, then the probability that he was guessing is ab \frac{a}{b} , where and b are co-prime integers. Find a+ba+b.

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