The Journal of Research of the National Institute of Standards

The Journal of Research of the National Institute of Standards and Technology (November-December 2003) published a study of a double intrusion detection system with independent systems. If there 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 with probability .2, and system B sounds an alarm with probability .1. Now assume that the probability of an intruder is .4. Also assume that under a given condition (intruder or not), systems A and B operate independently. If both systems sound an alarm, what is the probability that an intruder is detected?