# Infamous Birthday probability

**URL:** <https://boards.straightdope.com/t/infamous-birthday-probability/107942>\
**Category:** Factual Questions\
**Created:** [May 8, 2002, 6:47pm UTC](https://boards.straightdope.com/t/infamous-birthday-probability/107942 "2002-05-08T18:47:16Z")\
**Posts on this page:** 5\
**Page:** 2

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**Author:** ![Jabba](https://avatars.discourse-cdn.com/v4/letter/j/b5e925/32.png) [@Jabba](https://boards.straightdope.com/u/Jabba)\
**Post date:** [May 14, 2002, 11:07am UTC](https://boards.straightdope.com/t/infamous-birthday-probability/107942/21 "2002-05-14T11:07:10Z")

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Indeed, roughly 27% of classes of 31 people will not contain two people sharing a birthday.

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**Author:** ![Triskadecamus](https://avatars.discourse-cdn.com/v4/letter/t/b19c9b/32.png) [@Triskadecamus](https://boards.straightdope.com/u/Triskadecamus)\
**Post date:** [May 14, 2002, 2:04pm UTC](https://boards.straightdope.com/t/infamous-birthday-probability/107942/22 "2002-05-14T14:04:02Z")

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I think the chances are smaller than that.

Tris

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**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [May 14, 2002, 2:32pm UTC](https://boards.straightdope.com/t/infamous-birthday-probability/107942/23 "2002-05-14T14:32:53Z")

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No, **Jabba** is correct.

As I mentioned above, to find the probability that no two people share a birthday among n people:

## 365!

(365-n)! \* 365^n

For n=31, this is indeed about 27% (26.95…)

To find the probability that at least two share a birthday, subtract this from one.

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**Author:** ![GSV\_Consolation\_of\_Dreams](https://avatars.discourse-cdn.com/v4/letter/g/f1d935/32.png) [@GSV\_Consolation\_of\_Dreams](https://boards.straightdope.com/u/GSV_Consolation_of_Dreams)\
**Post date:** [May 14, 2002, 3:14pm UTC](https://boards.straightdope.com/t/infamous-birthday-probability/107942/24 "2002-05-14T15:14:19Z")

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This thread in general and **Cabbage’s** posts in particular have reminded me just how little I know about probability. :o

It’s been a few years since my Chemistry degree but still, I really need to brush up. Anyone in a similar situation might consider taking a gander at [this Basic Concepts page.](http://www.mala.bc.ca/~johnstoi/maybe/maybe1.htm)It’s designed for Liberal Arts students so it should be pretty gentle.

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**Author:** ![GSV\_Consolation\_of\_Dreams](https://avatars.discourse-cdn.com/v4/letter/g/f1d935/32.png) [@GSV\_Consolation\_of\_Dreams](https://boards.straightdope.com/u/GSV_Consolation_of_Dreams)\
**Post date:** [May 14, 2002, 3:26pm UTC](https://boards.straightdope.com/t/infamous-birthday-probability/107942/25 "2002-05-14T15:26:18Z")

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Dammit, 10 minutes and I think I may have picked the wrong paper.

> [@](#):
>
> Hence, if you are betting $1 that four heads will appear in a four-toss sequence of coins and if your opponent is unwilling to put up $15, you should not undertake the bet (the probabilities are against you). If she is willing to put up more than $15, then you should take the bet (the probabilities are in your favour).

But maybe I’m just nit-picking. The probabilities are still against you, but if you keep it up, your opponents betting should result in you being “ahead” at some point in the future.

/hijack.

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