It would be really interesting to see chances of being born across all time. Like what is the probability of being born here and now vs. somewhere else in the past or the future.
You would have to make some predictions based on population growth and maybe model a few different possible apocalypses (average species lifetime/meteor probabilities/nuclear doomsday/climate disaster etc.) but it would be a fun model to play with.
Yeah, population sizes overall would have been much smaller in the past, so paleolithic times would probably be comparitively insignificant (even 2000 years ago the entire population was less than 200 million and now it's 8 billion more than that).
I wonder if you could get a very rough statistical estimate of humanity's downfall just by assuming that we are somewhere in the middle of history. Like if I was born as a random person, I'm more likely to be born at a time where more people are born than when few people are born. So if you model that and make some assumptions about population growth/decline rates, could you put some numbers on when the last person is likely to be born within a margin of error?