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COMEDK2021MathematicsProbability

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is p, 0 < p < 1 . If he does not know the correct answer, he randomly ticks one answer. Given that he has answered the question correctly, the probability that he did not tick the answer randomly, is

Options

  1. A3 p 4 p+3
  2. B5 p 3 p+2
  3. C5 p 4 p+1
  4. D4 p 3 p+1

Correct answer

C. 5 p 4 p+1

Step-by-step solution

Let K be the event that the student knows the correct answer, and R be the event that the student ticks the answer randomly. Let C be the event that the student answers the question correctly. The probability that the student knows the answer is P(K) = p . The probability that the student does not know the answer is P(K^ c ) = 1 - p . If the student knows the answer, the probability of answering correctly is P(C|K) = 1 . If the student does not know the answer, the student ticks randomly among 5 alternatives, so th

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