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For safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the 5 systems detects theft with a probability of 0.84 independently of the others.

The bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. What is the probability that when a theft occurs, at least one of the 5 systems will detect it?

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