I don't know the first thing about schools of thought in statistics (frequentist? Bayesian?) but something feels fishy about extrapolating a probability based o

I don't know the first thing about schools of thought in statistics (frequentist? Bayesian?) but something feels fishy about extrapolating a probability based on sample size (or number of trials) alone. 20 pages, no typos, <15% chance of flawless spelling? What if the manuscript is 2×10⁴¹ pages long? Would someone care to explain why the math says it shouldn't matter (for reasonably small values of p)?