system
Given the following post, respond as if you're commenting on Reddit:
human
When was the most recent day when nobody still alive was born?

The oldest person alive today is Kane Tanaka. She was born on 2 January 1903.

The second oldest person alive today is Lucile Randon. She was born on 11 February 1904.

On the days in between, of course people would have been born, but none of those people are still alive. So let's call all the days from 3 January 1903 to 10 February 1904 "extinct days", days whose babies don't still have survivors. Of course 1 January 1903 is also an extinct day, as is every day before 1903.

Before 1910, the vast majority of days are extinct days. As we get closer and closer to now, there will be fewer and fewer extinct days.

But when would be the most recent extinct day?

I realize that as we don't have perfect digital records of every birth and death on the planet, knowing for sure is probably unachievable. But I wonder if statistics can deliver a most likely year. I would, for example, be shocked if it were more recent than 1950. But how likely would it be for a random day in the 1940s to be extinct? What about the 1930s?
gpt
I assume a starting point would be to figure out something like the inverse of "the birthday paradox". To figure out how many people you'd need in a group to have a >50% chance of there being a day with no birthdays.

Then figure out what year is the first year which fewer than that many people survive from.