Public schools and mass shootings?? (Kind of long)

Had this theory pop up in my mind and wanted to get the OT's opinion.
As they say, there are only 2 things that are 100%...death and taxes. So no matter what, there will always be these deranged school kids doing these things.
But I was wondering how many of these mass shootings (let's say since Columbine) have happened at a Private High School?? From what I understand, it's been almost, if not all, at the Public schools.
I personally think it's 2 reasons.
One, if parents have to pay a lot of money to send their kids to school, rather than for free, they tend to be more invested in a child and are more involved in the child's life.
Secondly, it's expensive to send a kid to a private school....which means a lot (not all) private school kids come from a 2 parent household. And studies show children who come from a 2 parent family, tend to adapt to life/the world better than a single family home.

I don't have any kids yet, first one is on the way now, but it is something I brought up to my wife last night. She said she wasn't sure, but it is an interesting thought.
Opinions??