What were the chances of the Apollo 11 mission failing? Consider the following scenarios: least one of the crewmembers dying, failing to land on the Moon, unable to return to Earth, the Soviets landing on the Moon first etc. Was it likely or improbable?
Most of your question is a duplicate; I'll address the "Soviets land first" question a bit, though that's a more subjective issue.
I don't think there was ever a significant chance that the USSR would beat the US to a moon landing. Development of the N1 moon rocket started in late '65, over three years behind the Saturn V; the chief designer, Korolev, died the next year. Before the first (failed) flight of the N1 in early '69, the US had already flown Apollo 8 around the moon; at that point it's likely that nothing short of losing a crew in an in-flight accident would have stopped the program, and likely not even that.
If Kennedy hadn't made his "before the decade is out" speech, things might have been different; NASA had always planned to go to the moon eventually but likely would have taken a slower, less dramatic course to get there, possibly focusing on space stations in Earth orbit in the late 60s and moon landing in the mid 70s. Without that pace, the USSR might have taken a slower and safer approach to the development of the N1, and it could have been closer.