In a test student either guesses or copies or knows the answer to a multiple choice questions with four choices in which exactly one choice is correct. The probability that he makes a guess is $\frac{1}{3}$ ; The probability that he copies the answer is $\frac{1}{6}$ . The probability that his answer is correct given that he copied it is $\frac{1}{8}$ . Find the probability that he knew the answer to the question given that he correctly answered, it is

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$\frac{1}{7}$

$\frac{1}{9}$

$\frac{24}{29}$

$\frac{29}{35}$

answer is B.

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Detailed Solution

Let ‘A’ be the event of guessing the correct answer. ‘B’ be the event of copying the correct answer. ‘C’ be the event of knowing the correct answer. ‘D’ be the event that his answer is correct

$\begin{array}{l} P (A) = \frac{1}{3} \\ P (B) = \frac{1}{6} \\ P (C) = \frac{1}{2} \\ P (\frac{D}{B}) = \frac{1}{8} \\ P (\frac{D}{A}) = \frac{1}{4} \\ P (\frac{D}{C}) = 1 \end{array}} P (\frac{C}{D}) = \frac{P (C) P (\frac{D}{C})}{P (D \cap A) + P (D \cap B) + P (D \cap C)} = \frac{24}{29}$