The probability that a student knows the correct answer to a multiple-choice question is \(\frac{2}{3}\). If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is \(\frac{1}{4}\). Given that the student has answered the question correctly, the probability that the student knows the correct answer is
A. \(\frac{5}{6}\)
B. \(\frac{6}{7}\)
C. \(\frac{7}{8}\)
D. \(\frac{8}{9}\)
Answer:D
The probability that a student knows the correct answer to a multiple-choice question is \(\frac{2}{3}\). If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is \(\frac{1}{4}\). Given that the student has answered the question correctly, the probability that the student knows the correct answer is
A. \(\frac{5}{6}\) B. \(\frac{6}{7}\) C. \(\frac{7}{8}\) D. \(\frac{8}{9}\)