SOLUTION: For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems will fail to dete

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Question 1084400: For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems will fail to detect theft with a probability of .01 independently of the others.The bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will fail to detect it. This probability is equal to:
   (.99)^4
   1 - (.99)^4
   (.01)^4
   1 - (.01)^4
   none of these

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

Pr(at least one systems fail to detect theft) = 1 - P(none of the systems fail to detect theft)
P(none of the systems fail to detect theft) = +%280.99%29%5E4+
So the answer is +1-%280.99%29%5E4+