Is it known whether probabilities of success vs failure (and specifically fatal failures) were estimated at the time for the Apollo XI mission? Or perhaps some current estimates?
Neil Armstrong thought they had a 90% chance of survival, but only a 50-50 chance of landing on the first attempt. I've seen one source that says Aldrin was less optimistic, estimating 2/3 chance of survival and 1/3 chance of success. At that time, Apollo spacecraft had flown several missions safely, including two lunar orbit missions, so presumably he was worried about the landing proper.
I've seen multiple references to a "three nines" goal per mission for crew safety, and either 90% or 99% for mission success. Presumably they got to those reliability estimates "on paper" by the time Apollo 11 flew.
Both those numbers seem pretty optimistic to me. In the end, the Apollo flights from 11 on had a 100% safety rate and 85.7% mission success rate, and Apollo 11 was probably the riskiest of that series.
Here's an early-1965 QA report giving the then-current probabilities of success as 0.73 and safety as 0.96, and presumably they got those numbers up over the next four years.
However, the individual failures experienced on the actual Apollo missions generally fell into the "unknown unknowns" category of interactions between individually-reliable subsystems, so I feel like the actual chances could have been quite a bit worse than what the analysts might have calculated.
If the manufactured parts for the Apollo spacecraft had a .1% failure rate the mission would have certainly failed. There were over 6,000,000 parts used. At .1% failure rate 600 individual parts would have failed.