A computer intrusion detection system (IDS) is designed to provide an alarm when

Question

A computer intrusion detection system (IDS) is designed to provide an alarm whenever an intrusion is being attempted into a computer system. Consider a double IDS with system A and system B. If there is an intruder, system A sounds an alarm with probability 0.94, and system B sounds an alarm with probability 0.96. If there is no intruder, the probability that system A sounds an alarm (i.e., a false alarm) is 0.21 and the probability that system B sounds an alarm is 0.11. (Let "A" be the event that alarm A sounds, "B" be the event that alarm B sounds, and "In" be the event of an intruder.) Complete parts a through d. thesynbalsgivenintheproblem statement, ex re“ e ie event ofanmoerprobatplete a. Using the symbols given in the problem statement, express the four probabilities given in the example. | = 0.94, = 0.96, | = 0.21. 1 =0.11 b. If there is an intruder, what is the probability that both systems sound an alarm? (Type an exact answer in simplified form.) c. If there is no intruder, what is the probability that both systems sound an alarm? (Type an exact answer in simplified form.) d. Given an intruder, what is the probability that at least one of the systems sounds an alarm? (Type an exact answer in simplified form.) Enter your answer in each of the answer boxes.

Explanation / Answer

(a) P(A/In) = 0.94, P(B/In) = 0.96, P(A/Inc) = 0.21, P(A/Inc) = 0.11. (Instead of Inc, it might also be given as In')

(b) Given there is an intruder, both alarms sound = 0.94 * 0.96 = 0.9024

(c) Given there is no intruder, both alarms sound = 0.21 * 0.11 = 0.0231

(d) Given there is an intruder, at least 1 alarm sounds = P(A sounds, B does not) + P(B Sounds, A does not) + P(Both Sounds) = (0.94 * 0.04) + (0.96 * 0.06) + (0.94 * 0.96) = 0.0376 + 0.0576 + 0.9024 = 0.9976

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