In a test, a student either guesses, copies, or knows the answer to a multiple-choice question with four choices, where exactly one choice is correct. The probability that the student makes a guess is

Question

In a test, a student either guesses, copies, or knows the answer to a multiple-choice question with four choices, where exactly one choice is correct. The probability that the student makes a guess is 3 1 ​ ; the probability that the student copies the answer is 6 1 ​ . The probability that the answer is correct, given that the student copied it, is 8 1 ​ . Find the probability that the student knew the answer to the question, given that they correctly answered it.

TestHub · Accepted Answer

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 $P (A) = \frac{1}{3} P (B) = \frac{1}{6} P (C) = \frac{1}{2} P (\frac{D}{B}) = \frac{1}{8} P (\frac{D}{A}) = \frac{1}{4} P (\frac{D}{C}) = 1}$

$P (\frac{C}{D}) = \frac{P ( C ) \cdot P ( \frac{D}{C} )}{P ( D \cap A ) + P ( D \cap B ) + P ( D \cap C )} = \frac{24}{29}$

Mathematics - Probability Question with Solution | TestHub

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