Showsni wrote:(Can I apply that to anything? Say, there's a 95% chance I won't live to see my 26 * 20 = 520th birthday? Does that mean there's a 5% chance I will?
No, it only works for uniform distributions. That's why the what-if talks in terms of sequentially ordering humans before bringing dates into it, because we're uniformly distributed by number from first to last human (one human per number), but not uniform by year of birth.
To know the probability of living to a certain age, you have to pick randomly by person. Picking randomly by age can't tell you anything about longevity. If I roll a die and get 100,and ask you to find me a 100-year old, how am I supposed to calculate from that the probability that people live to be 100?
If I choose a random person alive today, it will tell me something about the age distribution of people alive today. In particular, I'll be 95% confident that the person isn't among the youngest 5% (and there'll be a 5% chance that he is). This doesn't tell me about actual longevity, though. Guessing that 20 times more people are past age 10 than are younger than 10 is not the same as concluding that 20 times as much lifetime happens past age 10 than before it.
If I choose a random person who was born in 1800 and look at how long they lived, it will tell me something about life expectancy in 1800, but it still won't tell me what you thought. If I find someone who died at age 30, I can be 95% confident that she wasn't among the youngest 5% of people to die (and assign a 5% chance to the claim that she was). But I most definitely *can't* conclude that there's a 95% chance that she wasn't in her first 5% of the average life (with a 5% chance that she was). A population where 5% of people die evenly between 20 and 30, and where everyone else dies evenly between 30 and 40, has the 5th percentile at age 30, while the age at which someone has completed 5% of their whole life is less than age 2.
Edit 2, to put it more simply:
It is true that 5% of people are among the youngest 5% of people.
It is false that 5% of people are in the first 5% of their own lives.
The latter could only be concluded from a uniform distribution of deaths from age 0 to whatever the hard maximum is, along with an exactly constant population size, and this is not a reasonable assumption under any normal circumstances. The most reasonable assumption with no other information is probably one where the probability of dying in the next year is the same no matter your age, which leads to an exponential distribution. If you wish to figure out an aging function, you'd need more than one data point.