To be clear, the false negative here would be a student who has brought a gun to a school and the computer ignores it. That is a situation where potentially multiple people can be killed in a short amount of time. It is not far, far worse to send cops.
Depends on the false positive rate doesn't it. If police are being sent to storm a school every week due to a false positive, that is quite bad. And people will become conditioned to not care about reports of a gun at a school because of all the false positives.
For what I’m saying, no it doesn’t because I’m just comparing a single instance of false positive to a single instance of false negative. Neither is desirable.