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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 .75 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.

 Jan 10, 2017
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P(1 detects) = C(3,1)(.75)(.25)^2  =  9/64

 

P(2 detects) = C(3,2)(.75)^2(.25)  =  27/64

 

P(3 detects) = C(3,3)(.75)^3  =  27/64

 

 

P(at least one detects)  =    [ 9 + 27 + 27]  / 64   =  63 / 64

 

 

 

cool cool cool

 Jan 10, 2017

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