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      Question

      Three persons i.e. ‘P’, ‘Q’ and ‘R’, are

      given the same puzzle to solve. The probability that ‘P’, ‘Q’ and ‘R’ will solve the puzzle is (2/5), (3/4) and (5/6), respectively. Find the probability that exactly one of them will not solve the puzzle.
      A 49/120 Correct Answer Incorrect Answer
      B 61/120 Correct Answer Incorrect Answer
      C 53/120 Correct Answer Incorrect Answer
      D 13/24 Correct Answer Incorrect Answer
      E 19/40 Correct Answer Incorrect Answer

      Solution

      Probability of ‘P’ solving the puzzle = 2/5
      Therefore, probability of ‘P’ not solving the puzzle = 1 – (2/5) = 3/5
      Probability of ‘Q’ solving the puzzle = 3/4
      Therefore, probability of ‘Q’ not solving the puzzle = 1 – (3/4) = 1/4
      Probability of ‘R’ solving the puzzle = 5/6
      Therefore, probability of ‘R’ not solving the puzzle = 1 – (5/6) = 1/6
      Therefore, required probability = {(3/5) × (3/4) × (5/6)} + {(2/5) × (1/4) × (5/6)} + {(2/5) × (3/4) × (1/6)}
      = (45/120) + (10/120) + (6/120) = 61/120

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