Question

A computer intrusion detection system (IDS) is designed to provide an alarm whenever there is unauthorized access into a computer system. A probabilistic evaluation of a system with two independently operating intrusion detection systems (a double IDS) was published. Consider a double IDS with system A and B. If there is an intruder, A sounds an alarm with probability .9 and system B sounds an alarm with probability .95. If there is no intruder, the probability system A will sound an alarm is .2 and system B is .1
a). if there is an intruder, what is the probability that both systems sound an alarm?
b) given that there is an intruder, what is the probability that at least one of the systems sounds an alarm?

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