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AP EAMCET2012MathematicsProbability

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is 9 / 10 . If he gets the correct answer to a question, then the probability that he was guessing is

Options

  1. A37 40
  2. B1 37
  3. C36 37
  4. D1 9

Correct answer

B. 1 37

Step-by-step solution

Let E₁ : The event that the students knows the answer and E₂ : The event that the student guesses the answer P (E₁ )= 9 10 and P (E₂ )=1- 9 10 = 1 10 Let E : The answer is correct. The probability that the student answered correctly, given that he knows the answer i.e., P ( E E₁ )=1 The probability that the students answered correctly, given that he guessed is 1 4 . P ( E E₂ )= 1 4 By using Baye's theorem, aligned P ( E₂ E ) & = P ( E E₂ ) P (E₂ ) P ( E E₁ ) P (E₁ )+P ( E E₂ ) P (E₂ ) & = 1 4 1 10 1 9 10 + 1 4 1 10

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