Question
Three persons i.e. ‘X’, ‘Y’ and ‘Z’, are given
the same puzzle to solve. The probability that ‘X’, ‘Y’ and ‘Z’ will solve the puzzle is (4/7), (2/5) and (1/2), respectively. Find the probability that exactly one of them will not solve the puzzle.Solution
Probability of ‘X’ solving the puzzle = 4/7
Therefore, probability of ‘X’ not solving the puzzle = 1 – (4/7) = 3/7
Probability of ‘Y’ solving the puzzle = 2/5
Therefore, probability of ‘Y’ not solving the puzzle = 1 – (2/5) = 3/5
Probability of ‘Z’ solving the puzzle = 1/2
Therefore, probability of ‘Z’ not solving the puzzle = 1 – (1/2) = 1/2
Therefore, required probability = {(3/7) × (2/5) × (1/2)} + {(4/7) × (3/5) × (1/2)} + {(4/7) × (2/5) × (1/2)}
= (6/70) + (12/70) + (8/70) = 26/70 = 13/35
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