Question

In an entrance test, there are multiple choice questions. There are four possible answers to each question, only one of which 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 the probability that he was guessing is

• A. \(\frac{37}{40}\)
• B. \(\frac{1}{37}\)
• C. \(\frac{36}{37}\)
• D. \(\frac{1}{9}\)

Hint:

Use Bayes' theorem. A guess is correct with probability 1/4, and a known answer is always correct.

Answer 1

The Correct Option is B

Step 1: Imagine 1000 questions:
The student knows 900 and guesses 100.

Step 2: Count the correct answers:
Known: all 900 are correct. Guessed: one fourth of 100, which is 25, are correct. Total correct: 925.

Step 3: Take the guessed share:
Among the 925 correct answers, 25 came from guessing: $\frac{25}{925} = \frac1{37}$.

Step 4: Check the complement:
Knowing gives $\frac{900}{925} = \frac{36}{37}$, which is option (C), the opposite event.

Final Answer:
$\frac1{37}$, option (B). \[ \boxed{\frac{1}{37} \text{ (B)}} \]