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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.