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Probability that A will pass the exam is 1 4 , B will pass the exam is 2 5 and C will pass the exam is 2 3 . The probability that exactly one of them will pass the exam is

Options

  1. A2 5
  2. B3 20
  3. C9 20
  4. D4 5

Correct answer

C. 9 20

Step-by-step solution

P A = 1 4 , P B = 2 5 , P C = 2 3 ∵ A , B , C are independent events, then the probability that exactly one of them passes = P A ∩ B C ∩ C C + P A C ∩ B ∩ C C + P A C ∩ B C ∩ C = P A ⋅ P B C ⋅ P C C + P A C ⋅ P B ⋅ P C C + P A C P B C ⋅ P C = 1 4 × 3 5 × 1 3 + 3 4 × 2 5 × 1 3 + 3 4 × 3 5 × 2 3 = 9 20

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