A student participates in a quiz consisting solely of true-false questions and answers every question. The student is certain of the answers to some questions and guesses the answers to the remaining ones. Whenever the student is certain of an answer, they respond correctly. Assume that the probability of the student providing the correct answer when guessing is half. Additionally, assume that the probability that an answer was guessed, given that the student’s answer is correct, is one sixth. Then, the probability that the student knows the answer to a randomly selected question is \( \frac{x}{y} \). Determine the value of \( x + y \).

Probability

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