Since I never actually mentioned it, my source is a documentary on Netflix (I don't remember which one, and it very well may no longer be there). Buzz Aldrin was describing how they were testing components, and one part in particular was tested 6 times and failed 3 times. There were some other parts he mentioned, and when you multiplied the cascading failures it came out to a 1/6 chance of success (he didn't calculate that number, and he mentioned there were other parts as well where he didn't list the failure rates - my 10% number is a fuzzy guess).
I admit memories are fuzzy, but I distinctly remember him saying there was a single component with a 50% failure rate. I assume they upgraded this part (as well as others) for future missions.
Also let me be clear, the moon landing conspiracy theories have been debunked pretty thoroughly, and the landing has been documented in painstaking detail, but we should be mindful that such an incredible accomplishment will inspire incredulity. Like how some people think the great pyramids were made by aliens because how could such an ancient civilization build them. Our reaction to conspiracy theorists should be to debunk them and educate them, not to call them crazy. In this case, they aren’t crazy, because if someone tells you they went to the moon and returned, you are right to ask questions. (I’m not talking about bad-faith people who will deny all the evidence)
That doesn't seem very plausible, given that six missions brought astronauts to the moon (plus one that famously failed but returning all the crew to earth alive).
If the initial odds were under 1/6, what brought them so much higher in the following missions that you had seven in a row without loss of human life?