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A study of a double intrusion detection system with two independent monitoring systems was conducted. If there is an intruder, system A sounds an alarm with probability 0.85 and system B sounds an alarm with probability 0.95. If there is no intruder, system A sounds an alarm with probability 0.10 and system B sounds an alarm with probability 0.05. Now, assume that the probability of an intruder is 0.4. If both systems sound an alarm, what is the probability that there is an intruder?

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