At the end of every year, the TSA blogs about the weapons and explosives it prevented from getting on board airplanes. They are trying to brag about all the dangers they've stopped. But the opposite is true, when you do the math, you realize that they are stopping no dangers at all. The TSA stops less than half the bombs that get on board airplanes -- yet airplanes are not falling out of the sky due to the bombs that do get on board. Thus, mathematically, bombs aren't a danger. It therefore doesn't matter if the TSA stops bombs or not.
We know the TSA stops less than 50% of bad stuff from various sources. The first is the government's own tests, such as that described in a recent story where the TSA failed a shockingly 95% of the time.
Another is a statistic reported by the TSA where the number of firearms they stop every year is rapidly increasing. This does not match any other trend in society, such as the number of people carrying firearms. The only reason for such rapid growth is that the TSA gets better every year at detection. That means, historically, the TSA is letting an enormous number of firearms through. Since the graph isn't tapering off, we can assume they are still far from reaching 100%.
Lastly, there is anecdotes. I hear frequent stories of people arriving at their destination with knives and guns that they've accidentally carried through TSA security. Asking on twitter reveals many more. Lots of people admit to having carried loaded weapons through TSA security. Such stories are common -- but I've never heard of somebody getting caught -- being one of those counted in the TSA statistics in there charts. Anecdotal, albeit from small sample size, this seems to confirm that you have a less than 50% chance of getting caught.
This leads to a counter-intuitive result that the TSA is really not stopping any danger. If guns and bombs are getting on planes, but planes aren't falling out of the sky, it must mean that they aren't a danger.
I point this out because in the end, safety is an emotional thing rather than logical. No matter how much I do the math, people do not believe it. They believe bombs are a danger to airplanes in much the same way many don't believe the safety statistics compared to driving.
Of course, this does not necessarily prove the TSA is ineffective. The security theater may discourage terrorist wannabes. Also, racist profiling may be more effective at stopping certain weapons than for the general population. I have an Iranian friend who apparently gets felt up every flight [which, separate from math, makes we want to say "fuck you TSA"].
But I suspect the TSA really is useless. I suspect the real reason that terrorists haven't taken planes out of the sky is that it frankly isn't that great of a threat, and that the existence of the TSA is simply because police-states gonna police-state.