In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then what is the probability that he was guessing ?
- A. \frac{37}{40}
- B. \frac{36}{37}
- C. \frac{1}{37} ✓
- D. \frac{1}{40}
Correct Answer: C. \frac{1}{37}
Explanation
P(Knows) = 0.9, P(Guesses) = 0.1. P(Correct|Knows) = 1, P(Correct|Guesses) = 1/4 = 0.25. By Bayes' Theorem, P(Guesses|Correct) = (0.1 * 0.25) / (0.9 * 1 + 0.1 * 0.25) = 0.025 / 0.925 = 1/37.
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