申論題

4. GuardWare Inc. has installed intrusion-detection devices on the campus of a large university.
The devices are very sensitive and, on any given weekend, each one has a 10% chance of being mistakenly activated when no intruder is present. Assume that the mistaken activations of different devices are independent events.
There are six devices in the Administration building. Assume there will be no intruder in that building next weekend.

(b) An intruder has a 5% chance of not activating the device located in the President's office.
Campus police has obtained information about a student prank in preparation and, as a result, estimates that there is a 20% chance that an intruder will visit the President's office during next Columbus Day weekend. If this device is activated during that weekend, what is the probability that there is an intruder in the President's office? Answer=__(L)__