In an examination, an examinee either guesses or copies or knows the answer to a multiple-choice question with four choices. The probability that he makes a guess is (1/3) and the probability that be copies the answer is (1/6). The probability that his answer is correct, given that he copied it , is (1/8). The probability that his answer is correct, given that he guessed it, is (1/4). Find the probability that he knew the answer to the question, given that he correctly answered it.

Explanation

To solve the problem, we will use Bayes' Theorem to find the probability that the examinee knew the answer given that he answered correctly. We will denote the events as follows:

- Let \( E_1 \): the event that the examinee guesses the answer.
- Let \( E_2 \): the event that the examinee copies the answer.
- Let \( E_3 \): the event that the examinee knows the answer.
- Let \( C \): the event that the examinee answers correctly.

Given probabilities:
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