While in community college, I was in a physics class whose lab instructor had worked for NASA under Dr. Von Braun. Once I learned of that, everything other than the moon mission became trivial. I pummelled the poor guy with as many technical questions I could find.
He said there was a 1/10,000 chance of mission failure; that is of the crew not returning to Earth safely. That may seem good, but if you were told that there was that same chance of your airliner going down, would you board it?
The rockets employed a backup system that compared the voltages between three devices, that were used to aim the gimball-mounted exhaust nozzles. if the primary one differed from the test one, the circuit switched to the third one. There was no secondary backup.
It is indeed rather sad that people of this generation do not realize just how very different life was even a few years ago.