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@ Accidental shootings vs. Home invasion defense stats:
Consider the following: Let's say you have a 99% chance of correctly identifying a home invader on a given night (so you have a 1% chance of not identifying him, and a 1% chance of also falsely identifying someone as a home invader) and you have a 1% chance of having your house attacked by a home invader in a given year.
That means that over a given year, with 365 nights, you will have on average 0.01 home invasion incidents(only happens to you one year in a hundred), but you will have 3.65 occasions where you falsely identify a home invader (false positive).
This means that if you believe there is a home invader, there's a 0.2% (0.01/3.66) chance that what you have identified is in fact a home invader.
Let's be a bit more pessimistic, and say that you on average have a home invasion incident once every year, then it will be 1/4.65, or only 20% chance of any given incident actually being a home invader. With 99% accuracy you would need to expect more then 3 such incidents in a given year before you broke even in correctly identifying a thief.
As a side note, it's this math that's the reason your burglar alarm is always going off without there being any actual burglar. When an event is rare, false positives are much more likely then correct identifications.
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