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

Question 1084395: 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. What is the probability that when a theft occurs, none of four systems will detect it?
�� (.99)^4
�� (.01)^4
�� (.01) * 4
�� 4 * (.01) * (.99)^3
�� 4 * (.99) * (.01)^3

Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
The probability of failure is .01, so the probability that all four will fail at the same time is .01x.01x.01x.01, or (.01)^4, which equals 0.00000001. ☺☺☺☺
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