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Let P 1 , P 2 and P 3 are the probabilities of a student passing three independent exams A , B and C respectively. If P 1 , P 2 and P 3 are the roots of equation 20 x 3 - 27 x 2 + 14 x - 2 = 0 , then the probability that the student passes in exactly one of A , B and C is

Options

  1. A3 20
  2. B7 20
  3. C1 4
  4. D1 5

Correct answer

C. 1 4

Step-by-step solution

P 1 + P 2 + P 3 = 27 20 P 1 P 2 + P 2 P 3 + P 3 P 1 = 14 20 P 1 P 2 P 3 = 2 20 Probability that the student passes in exactly one of A , B , C is = P 1 + P 2 + P 3 - 2 P 1 P 2 + P 2 P 3 + P 3 P 1 + 3 P 1 P 2 P 3 = 27 20 - 2 14 20 + 6 20 = 5 20 = 1 4

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