90 Intrusion detection systems. A computer intrusion detection system (IDS) is designed to provide an alarm whenever someone intrudes (e.g., through unauthorized access)

into a computer system. A probabilistic evaluation of a system with two independently operating intrusion detection systems (a double IDS) was published in the Journal of Research of the National Institute of Standards and Technology (Nov.–Dec. 2003). Consider a double IDS with system A and system B. 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, the probability that system A sounds an alarm (i.e., a false alarm) is .2 and the probability that system B sounds an alarm is .1.

a. Use symbols to express the four probabilities just given.

b. If there is an intruder, what is the probability that both systems sound an alarm?

c. If there is no intruder, what is the probability that both systems sound an alarm?

d. Given that there is an intruder, what is the probability that at least one of the systems sounds an alarm?