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COMEDK202510 May 2025Morning ShiftMathematicsProbabilityActual

In an entrance test, there are multiple choice questions. There are four possible answers to 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 the probability that he was guessing is

Options

  1. A36 37
  2. B1 37
  3. C1 9
  4. D37 40

Correct answer

B. 1 37

Step-by-step solution

Let K be the event that the student knows the answer and G be the event that the student guesses the answer. Let C be the event that the student gets the correct answer. Given P(K) = 0.9 and P(G) = 1 - 0.9 = 0.1 . If the student knows the answer, the probability of getting it correct is P(C|K) = 1 . If the student guesses, there are 4 options and only 1 is correct, so the probability of getting it correct is P(C|G) = 1 4 = 0.25 . The total probability of getting the correct answer is P(C) = P(C|K)P(K) + P(C|G)P(G)

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