If The System tells me that contraceptions are X% effective, and I believe them, and it's true, the problem remains of the failure rate. That's unrelated to trust.
That's maybe mostly a semantic quibble about the precise meaning of trust. I don't think it's considered absurd to say "I trust that my plane won't crash" when flying. Maybe it's more usual to say "I hope that my plane won't crash". It appears to be the case that we "hope" if we don't see the social dimension of the phenomenon we are referring to, while "trust" is also communicates a stronger social dimension.
Note also that in interactions with humans, we generally don't have a precise probabilities.
