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Chapter 8: Q92E (page 452)

Intrusion detection systems. The Journal of Researchof the National Institute of Standards and Technology (November–December 2003) published a study of a doubleintrusion detection system with independent systems. Ifthere is an intruder, system A sounds an alarm with probability.9, and system B sounds an alarm with probability.95. If there is no intruder, system A sounds an alarm withprobability .2, and system B sounds an alarm with probability.1. Now assume that the probability of an intruderis .4. Also assume that under a given condition (intruderor not), systems A and B operate independently. If bothsystems sound an alarm, what is the probability that anintruder is detected?

Short Answer

Expert verified

The probability that anintruder is detected is 0.9661.

Step by step solution

01

Important formula

The formula for probability isP=favourableoutcomestotaloutcomes.

The Baye’s formula is

P(BiA)=P(Bi⌒A)P(A)=P(Bi)P(ABi)P(B1)P(ABi)+P(B2)P(AB2)+...+P(Bk)P(ABk)

02

The probability that anintruder is detected

Let,

A=intruder

B=system A sounds alarm

C=system B sounds alarm

PA=0.4PB\A=0.9PC\A=0.95PB\Ac=0.2PC\Ac=0.1

The systems are independent.

PB⌒C\A=0.9×0.95=0.855

PB⌒A\Ac=0.2×0.1=0.02

By using Baye’s rule, if both systems sound an alarm, the probability that an intruder is detected obtained as:

PA\B⌒C=0.855×0.40.855×0.4+0.02×0.6=0.9661

Therefore, the likelihood of spotting an intruder is 0.9661.

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