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.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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