SOLUTION: 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 pr
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Question 1123951: 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 0.8 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? Answer by ikleyn(52781) (Show Source):
For each single system of five, the probability that it will not detect a theft is the complement to 0.8, i.e. 1-0.8 = 0.2.
The probability that NO ONE of five systems will detect a theft is {{0.2^5}}} = 0.00032.
The probability that when a theft occurs, at least one of the 5 systems will detect it is THE COMPLEMENT to it, i.e. 1 - 0.00032 = 0.99968.
