I do know, to within an epsilon and delta.

I can show you the unfavorable statistics for any and all numbers less than that if you so wish. Each one is unfavorable.
I didn't imply you are wrong. I said outright you are wrong. I also didn't say you were wrong because you didn't understand an unrelated example. I said you were wrong because it appears you lack a firm grasp of the field of statistics, and then used an example to point out how that's not uncommon because statistics often goes against common sense, and that I was thusly unsurprised that you lacked a firm grasp on statistics.
I don't have to since that's not strictly true and also racial profiling is illegal.
I never said anything about being scarred emotionally. I said economic, privacy, and social costs. Nothing about emotional costs.
I will never forgive the admins for removing the roll eyes emoticon.
We do this system exactly for the opposite reason why we have the automated terrorist search system in place: we value letting an innocent man stay free over convicting a guilty man. THat's the exact opposite of these terrorist systems. As such, it's a cost we shoulder as a social collective because we see the cost as being worth it. That is not the case with these automated systems which violate "innocent until proven guilty" on a fundamental level.
There is only three variables to account for: pool size, target size, and error rate. The large pool size, the small amount of terrorists in he US, and the fact that there is an error rate associated with every automated system makes it the case with an absolute probabilistic unfavorable outcome.
But it's not limited to arbitrary factors. The base line fallacy is PROVEN EMPIRICALLY to ALWAYS exist whenever you have ANY large pool from which you are drawing samples where the target is only a small percentage.