If you add up all the information disseminated by our government in the last 100 years, I don't think even half of it turned out to be factually correct in the end, meaning less truthful than randomness.
This implies a 50% chance that a randomly generated statement is true, which--without getting into the weeds on the generative model--is certainly false.
For example, I can generate random statements of the form "I am X years old" for X \in {1, ..., 100}.
Far from a 50% chance that the statement is factually correct.
No, that very much depends on the weeds of the generative model. I can generate random statements of the form "I am not X years old" for X \in {1, ..., 100}.
-Homer Simpson