Conversely humans are absurdly bad at statistics - i.e. "an astronaut feels he has a 50 to 70% chance of success"...isn't a real prediction. It isn't based on any failure analysis.
The actual failure analysis and engineering was substantially more confident, because otherwise why go? 50% is a coin-flip, but those odds were already proven wrong by the missions before Apollo 11 anyway (since there was more then 1).
You're doing some improv here based on your intuition when history has a way of surprising us. So what was the "actual" failure analysis and risk percent? It didn't exist. "Mathematical risk analysis was used in Apollo, but it gave unacceptably pessimistic results and was discontinued." [1]
Of course there were working assessments internally and they generally put the figure at about 50%. That figure is from Gene Krantz's excellent book "Failure Is Not an Option." The reason you go is because you cannot find any other practical way to significantly reduce the risk, and are willing to accept the risk you end up with.
Also I feel you're somewhat denigrating the astronauts with your comment by saying their estimations weren't "real". These weren't just adrenaline junkies looking for a wild ride - they were extreme intellectual outliers with higher degrees in aerospace engineering and extensive backgrounds in the development and application/flight of all sorts of aerospace systems. Like that paper also mentions, "The only possible explanation for the astonishing success [of the Apollo Program] – no losses in space and on time – was that every participant at every level in every area far exceeded the norm of human capabilities."
The actual failure analysis and engineering was substantially more confident, because otherwise why go? 50% is a coin-flip, but those odds were already proven wrong by the missions before Apollo 11 anyway (since there was more then 1).