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Comment by CapriciousCptl | Hacker News Reader

One of Warren Buffett's primary fears is weapons of mass destruction, I think since the 70s (as stated in his semi-autobiography, Snowball). During the cold-war, he put things like this (paraphrasing from memory): if there's a 4% chance of nuclear war per annum, there's a 70% chance of it happening over the next 30 years. If we reduce the annual chance to 2%, we reduce the 30-year chance to 45%.

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for some reason those numbers are not adding up to me. do the chances compound year-over-year? how is the 4% any different in year 1 than in year 30? or any year in between? how does this add up to 70% over a 30 year period

If you assume 4% each year independently of each other year, then the chance of not having nuclear war is 96% in any given year. Over 30 years, your chance of no war is (0.96)^30 = 30%.

> If you assume 4% each year independently of each other year, then the chance of not having nuclear war is 96% in any given year. Over 30 years, your chance of no war is (0.96)^30 = 30%.

It's clearly not independent though, but this calculation remains true if you assume only that not having a nuclear war doesn't change the odds for future years, even if having one does.

My apologies, you are right -- I should have said "4% each year independently of each prior year" -- and it's true that only the negation needs to be independent.

You can try it yourself without any of the math with just a little bit of programming.

  function calc30(odds) {
    for (let i = 0; i < 30; i++) {
      if (Math.random() < odds) return true;
    }
    return false;
  }
  Array.from(Array(10000)).map(() => calc30(0.04)).filter(Boolean).length //=> 7022 or ~70%
  Array.from(Array(10000)).map(() => calc30(0.02)).filter(Boolean).length //=> 4545 or ~45%

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