A company has installed five intrusion-detection devices in an office building. The devices are very sensitive and, on any given night, each one has a 0.1 probability of mistakenly sounding an alarm when no intruder is present.
If two or more of the devices are activated on the same night, the intrusion system automatically sends a signal to the local police.
If no intruder is present on a given night, what is the probability that the system will make the mistake of calling the police?