[jamestnz]

>How long something has been around is often a good way to determine how much longer it will be around in the future

This mode of (purely statistical) longevity argument is the "Doomsday Argument". The classic version is about predicting how much longer human civilization might endure. The crux of it is that there's only a 5% chance that we're currently in the first 5% of humanity's total timeline, and a 95% chance that we're in the last 95% of it.

If we assume that 60 billion humans have been born so far, it can be estimated that there is a 95% chance that the total number of humans ever will be less than 20 × 60 billion = 1.2 trillion. Assuming that the world population stabilizes at 10 billion and a life expectancy of 80 years, it can be estimated that the remaining 1,140 billion humans will be born in 9,120 years.

https://en.wikipedia.org/wiki/Doomsday_argument