Prolonged continuation of low probability

"If the chance of a nuclear war occurring in any given year is only 1 percent, then the chance of a nuclear war occurring within 1 00 years is fully 63 percent; within 200 years, 87 percent: and within 400 years 98 percent. The sufficiently prolonged continuation of a low probability makes a given outcome inevitable”.

How did the author arrive at these probabilities? (They are correct)

Is nuclear war inevitable? Why might you not accept the conclusions even if the statistical calculations are correct?

If \(\displaystyle p=0.01\), then \(\displaystyle 1-(1-p)^{100} = 0.634\), for example.