A student knows the answer to a multiple-choice question (with 4 options) with probability 3/4, or guesses with probability 1/4. If the student answers correctly, the probability they actually knew the answer is:
A student knows the answer to a multiple-choice question (with 4 options) with probability 3/4, or guesses with probability 1/4. If the student answers correctly, the probability they actually knew the answer is:
- A. 3/4
- B. 12/13
- C. 1/4
- D. 1/13
Answer: B) 12/13
Explanation: P(Know|Correct) = [P(Correct|Know)×P(Know)] / [P(Correct|Know)×P(Know) + P(Correct|Guess)×P(Guess)] = (1 × 3/4) / [(1 × 3/4) + (1/4 × 1/4)] = 12/13.
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