Question
Three persons i.e. ‘D’, ‘E’ and ‘F’, are given
the same puzzle to solve. The probability that ‘D’, ‘E’ and ‘F’ will solve the puzzle is (5/8), (2/3) and (3/5), respectively. Find the probability that exactly one of them will not solve the puzzle.Solution
Probability of ‘D’ solving the puzzle = 5/8
Therefore, probability of ‘D’ not solving the puzzle = 1 – (5/8) = 3/8
Probability of ‘E’ solving the puzzle = 2/3
Therefore, probability of ‘E’ not solving the puzzle = 1 – (2/3) = 1/3
Probability of ‘F’ solving the puzzle = 3/5
Therefore, probability of ‘F’ not solving the puzzle = 1 – (3/5) = 2/5
Therefore, required probability = {(3/8) × (2/3) × (3/5)} + {(5/8) × (1/3) × (3/5)} + {(5/8) × (2/3) × (2/5)}
= (18/120) + (15/120) + (20/120) = 53/120
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