[dunkmaster]

The birthday paradox works because you are looking for a pair that has the same birthday, regardless of what date that birthday is. It doesn't work in the habitable planet sense because you would be essentially locking the birthday to a fixed date.

[metalchianti]

Yes. How many people do you need in a room to be confident that one of them has the same birthday as you?

[EGreg]

Assuming a uniform distribution, the probability is 1/365 for any person#. Those probabilities add up linearly if the people are guaranteed to have different birthdays (union/OR). Otherwise the probability of NOT having someone with the same birthday goes down exponentially as a an exponential power of the fraction 364/365 (intersection of complement/AND NOT)

It’s exactly what you would expect from classical combinatorics with cards with or without replacement. Your term “confident” is vague.

I produced a series called Thinking Mathematically on youtube that makes all of this and other related topics clear for anyone... I recommend checking it out!

https://m.youtube.com/channel/UCuge8p-oYsKSU0rDMy7jJlA

And here are the notes for it

http://magarshak.com/math/numbers.pdf

http://magarshak.com/math/sets.pdf

http://magarshak.com/math/logic.pdf

# if we exclude all people born leap years

[vageli]

> Assuming a uniform distribution, the probability is 1/365 for any person#. Those probabilities add up linearly if the people are guaranteed to have different birthdays (union/OR). Otherwise the probability of NOT having someone with the same birthday goes down exponentially as a an exponential power of the fraction 364/365 (intersection of complement/AND NOT)

Why would we assume a uniform distribution of birthdays? For example, birthdays occurring on the 31st of a month are probably less likely to occur on average given that every month does not have 31 days. This is just one example and doesn't even go into seasonality of conception cycles.

[EGreg]

To simplify. Mathematical models don’t perfectly capture all the details usually.

[SamBam]

You need 253 people in the room to have > 50% probability that one will have the same birthday as you.

1 - ((365 - 1)/365)^253 = 0.5005

[uncoder0]

If birthdays are assumed to be distributed symmetrically. If you were born in august you'd need ~12 fewer people and for April you'd need ~12 more.[1]

Not sure how that looks for the worlds population probably averages out pretty well regardless.

[1]: https://www.panix.com/~murphy/bday.html

[isostatic]

How confident? Even with an even distribution of birthdays it's possible to have a billion people in the room that don't share your birthday. Very unlikely, but as there's only about 20 million people with your birthday, and 7 billion without, it's quite doable.

[dwaltrip]

"Very unlikely" is a severe understatement. With only 100k people, the odds of no one else having your birthday is 10^-120. With a million people, it is 10^-1192.

And with a billion people... apparently, there are over a million zeroes between the decimal place and the first non-zero number. That is a pretty damn small probability.

Here is the code I used in python 3:

   from decimal import Decimal
   print((Decimal(364) / Decimal(365)) ** num_people)

[isostatic]

quite, hence "how confident"

There's other things as play. Imagine you, born on July 15th, walked into a room with 1000 people. You'd be fairly confident someone will be born on July 15?

What if I then told you it was the annual astrology get together of Capricorns?

[dwaltrip]

Sure, but you did say "even distribution".

[MR4D]

I'm locking the area to a specific region. If I divide the universe into 365 discrete areas, the problem is exactly the same.

[dunkmaster]

If you're locking the area to a fixed area out of the 365 discrete areas, the birthday paradox isn't applicable anymore. Birthday paradox only says something about whether a pair exists among all areas.

[ithkuil]

So you're in a room with N people and learn that somebody else shares your birthday. Can you conclude that is this likely that other people in the room also share the birthday with somebody else?

[roywiggins]

If you already assume the room is a representative sample from a population where birthdays are uniformly distributed, it doesn't tell you anything.

But if you aren't certain about that, it makes it less likely that everyone else with your birthday has been ritually murdered or otherwise systematically excluded from the room, and slightly more likely that you're at a convention dedicated to people with your birthday.

[MR4D]

Thanks for posting. This is exactly what I was trying to say (but you said it better).