[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

[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

[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.

[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.