A highsecurity government installation has installed 3 secur

A high-security government installation has installed 3 security systems to detect attempted break-ins. The 3 security systems operate independently of each other, and each has a .85 probability of detecting an attempted break-in. Assume an attempted break-in occurs. Use the binomial distribution to find the probability that at least one of the 3 security systems will detect it. (Round your answer to 4 decimal places.)

Solution

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    3      
p = the probability of a success =    0.85      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.003375

Thus,

P(at least 1) = 1 - P(0) = 0.996625 [ANSWER]