Another issue with this logic is that the probabilities are not independent.
Saying that you have probability x of nuclear war every year and so probability (1-x)^n of no nuclear war in n years assumes independence. In fact, if you don't have nuclear war on year 1, I would assume that the reasons for that lead to inferences and correlations that would affect the probability of nuclear war on year 2, possibly making it lower.
Saying that you have probability x of nuclear war every year and so probability (1-x)^n of no nuclear war in n years assumes independence. In fact, if you don't have nuclear war on year 1, I would assume that the reasons for that lead to inferences and correlations that would affect the probability of nuclear war on year 2, possibly making it lower.