This makes very little sense to me. Nuclear war is not a random event that might happen at any given point with some probability P. It is a decision that is mad

This makes very little sense to me. Nuclear war is not a random event that might happen at any given point with some probability P. It is a decision that is made based on an evolving situation, there are not independent random event you can apply high school math to. Also an event being rare does not mean that it is unlikely. For example a 29th of February is a rare event, if you were to think about it in terms of probabilities, there is about 0.07% of chance for it to occur on any given day. So you would conclude that there is about 1-(1-.0007)^(2*365)=40% chance to occur within 2 years. But it is obviously absurd to think this way, since the next 29th of February will happen in 2024, in less than 2 years, the probability is 100%.