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      Question

      Three persons i.e. ‘M’, ‘N’ and ‘O’, are given

      the same puzzle to solve. The probability that ‘M’, ‘N’ and ‘O’ will solve the puzzle is (7/10), (3/5) and (1/2), respectively. Find the probability that exactly one of them will not solve the puzzle.
      A 9/25 Correct Answer Incorrect Answer
      B 11/25 Correct Answer Incorrect Answer
      C 53/100 Correct Answer Incorrect Answer
      D 12/25 Correct Answer Incorrect Answer
      E 13/25 Correct Answer Incorrect Answer

      Solution

      Probability of ‘M’ solving the puzzle = 7/10
      Therefore, probability of ‘M’ not solving the puzzle = 1 – (7/10) = 3/10
      Probability of ‘N’ solving the puzzle = 3/5
      Therefore, probability of ‘N’ not solving the puzzle = 1 – (3/5) = 2/5
      Probability of ‘O’ solving the puzzle = 1/2
      Therefore, probability of ‘O’ not solving the puzzle = 1 – (1/2) = 1/2
      Therefore, required probability = {(3/10) × (3/5) × (1/2)} + {(7/10) × (2/5) × (1/2)} + {(7/10) × (3/5) × (1/2)}
      = (9/100) + (14/100) + (21/100) = 44/100 = 11/25

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