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A lift will return to the ground floor in the event of a fire being detected. A voting system is designed with four identical fire

A lift will return to the ground floor in the event of a fire being detected. A voting system is designed with four identical fire detectors; and the lift returns to the ground floor if two or more detectors indicate a fire. Let p1 be the probability that this type of detector fails to detect a real fire; and let p1=0.001 (i.e. 1 in 1000). What is the chance of the lift return failing to occur in the event of a real fire?

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