# Chances of 2 people sharing a birthday=50%? **URL:** \ **Category:** Factual Questions\ **Created:** [September 29, 2004, 3:35pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675 "2004-09-29T15:35:38Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [September 30, 2004, 4:08am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/21 "2004-09-30T04:08:12Z")
> [@clairobscur](#): > > When he wrote “100%” the poster meant that since it’s already an established fact, it’s probability is 100%. I know that. But what does confirmation bias have to do with it? ---
**Author:** ![moggyAU](https://avatars.discourse-cdn.com/v4/letter/m/a6a055/32.png) [@moggyAU](https://boards.straightdope.com/u/moggyAU)\ **Post date:** [September 30, 2004, 5:58am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/22 "2004-09-30T05:58:23Z")
hmm i dont think its that rare, i have a friend who has the same birthday as his brother and the were bron 2 years apart. I have the same birthday as my aunt My gf has the same birthday as my best mate in fact i know many people who share the same birthday, some born in the same hospital on the same day and same year ---
**Author:** ![snailboy](https://avatars.discourse-cdn.com/v4/letter/s/97f17d/32.png) [@snailboy](https://boards.straightdope.com/u/snailboy)\ **Post date:** [September 30, 2004, 7:02am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/23 "2004-09-30T07:02:34Z")
I’ve never met anyone with the same birthday as myself (although I hear Cher shares it). On the other hand, I’ve never went around asking my classmates their birthdays. ---
**Author:** ![t-keela](https://avatars.discourse-cdn.com/v4/letter/t/a3d4f5/32.png) [@t-keela](https://boards.straightdope.com/u/t-keela)\ **Post date:** [September 30, 2004, 7:08am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/24 "2004-09-30T07:08:01Z")
> [@legion](#): > > I read somewhere once that in a class of 30 children the chances of 2 of the children sharing a birthday are about 50/50. > > Is this correct and if it is, why is it? First of all. A classroom of kids is not a random sample. Since it is a classroom the odds are nearly 100% that they will be the same age. So the birth year is practically a given. There are other restrictions in a classroom setting which increases the odds of an exact month. Cuttoff months and days for advancement as an example. I don’t recall the exact month but there is usually a specific date that is the cutoff date for the age at which a child can start school. **All of that aside…** the biggest variable which can be applied to even a random sample is the fact that there are times when people simply have sex more often than others. Like Valentine’s day for instance. Practically every new married couple is going to have sex on Valentines Day. Combine all these things and the odds are increased that two kids in a classroom will have the same date of birth. somewhere in mid-late October. Then there’s June newliweds and Christmas etc. but V-tines is the biggie. In my own family (extended as well) there are at least a dozen birthdays that month. ---
**Author:** ![t-keela](https://avatars.discourse-cdn.com/v4/letter/t/a3d4f5/32.png) [@t-keela](https://boards.straightdope.com/u/t-keela)\ **Post date:** [September 30, 2004, 7:12am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/25 "2004-09-30T07:12:16Z")
Sorry…that should’ve been November…you know about **nine months after Valentines day** sheesh… sleep…get some sleep… :smack: ---
**Author:** ![t-keela](https://avatars.discourse-cdn.com/v4/letter/t/a3d4f5/32.png) [@t-keela](https://boards.straightdope.com/u/t-keela)\ **Post date:** [September 30, 2004, 7:17am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/26 "2004-09-30T07:17:13Z")
I meant to add …I remember why I was thinking October now. There’s another big cluster nine months after New Years Eve. A really big cluster because of so many folks getting drunk and romantic etc… and forgetting to do anything about their birth control. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [September 30, 2004, 7:46am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/27 "2004-09-30T07:46:12Z")
> [@Mississippienne](#): > > I don’t care a whit about confirmation bias, I was asking what the odds were for 2 people in any random grouping of 15 to share the exact same birthdate. The 25% figure doesn’t measure an exact match, just from the 365 dates of a (non-leap) year. For an “exact” match, you’d have to compile demographic information and make the assumption that the people in the group are selected truly randomly (i.e. they not members of a class or peer group or anything else which would put them all of a particular age). At this point, it gets exceedingly complicated, as multivariate statistics loves to do, so I’ll just add some extra assumptions to make it workable: [ul][li]Everyone is American[/li][li]Everyone in the group is known to be at least 20 years old and less than 70 years old [/ul][/li] Relevant informtion from the 2000 census, dividing the U.S. population into groups by age: ```auto 20- 24 19,185,063 25- 29 19,316,817 30- 34 20,587,073 35- 39 22,648,354 40- 44 22,535,368 45- 49 20,230,558 50- 54 17,790,616 55- 59 13,559,151 60- 64 10,864,730 65- 69 9,533,955 ``` These people have birthdays across a fifty-year span, representing 18,264 birthdays. Trouble is, the numbers show that these birthdays are not evenly distributed among this population. The 50+ groups show a marked decline in numbers (for obvious reasons). So just for laughs let’s eliminate them and assume everyone in the sample is 20-49, whose numbers are reasonably consistant. ```auto 20- 24 19,185,063 25- 29 19,316,817 30- 34 20,587,073 35- 39 22,648,354 40- 44 22,535,368 45- 49 20,230,558 ``` This thirty-year span now comprises 10,963 birthdays, and we’ll assume for simplcity that they’re evenly distributed (they obviously aren’t, but bear with me). The odds of two out of 15 randomly-selected persons sharing an exact birthday are as follows: 1 - (10963!) / (10963-15)! (10963[sup]15[/sup]) ~= 1 - 0.9905 = 0.0095, or less than one percent. You’d have to sample 124 people before the odds of getting a match were more than 50%, which I’ll admit sounds low, but the math seems accurate enough. ---
**Author:** ![Pushkin](https://avatars.discourse-cdn.com/v4/letter/p/ee59a6/32.png) [@Pushkin](https://boards.straightdope.com/u/Pushkin)\ **Post date:** [September 30, 2004, 10:55am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/28 "2004-09-30T10:55:13Z")
> [@t-keela](#): > > I meant to add …I remember why I was thinking October now. There’s another big cluster nine months after New Years Eve. A really big cluster because of so many folks getting drunk and romantic etc… > and forgetting to do anything about their birth control. Yeah, the ozzie temp who shared my birthday said we were probably both conceived around New Years or possibly on it. Not that I like to think when or where my parents are at it, but nice to know that I was born of good spirits as the ozzie chick put it 🆒 ---
**Author:** ![vanilla](https://avatars.discourse-cdn.com/v4/letter/v/f19dbf/32.png) [@vanilla](https://boards.straightdope.com/u/vanilla)\ **Post date:** [September 30, 2004, 1:10pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/29 "2004-09-30T13:10:42Z")
I don’t believe it at all. I have our church directory, which lists everyones birthdays. There are about 160 members. No one has the same birthday. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [September 30, 2004, 1:57pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/30 "2004-09-30T13:57:07Z")
**vanilla** , the chances of that happening are 0.000000000000000099671433849300578506753494359707 %. To be honest, I don’t believe you (unless your church has some strange policy, like not accepting new members if they have the same birthday as an already existing member). Maybe you should check the directory again. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [September 30, 2004, 2:02pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/31 "2004-09-30T14:02:47Z")
But it just occurred to me, **Vanilla** , that maybe you’re not understanding the problem. The claims made in this thread are not about someone having the same birthday as **you** ; the claim is that, out of the 160 people in your church directory, there will be two people with the same birthday (month and day, not necessarily year)–you, however, might not be one of those two people. ---
**Author:** ![missbunny](https://avatars.discourse-cdn.com/v4/letter/m/76d3ee/32.png) [@missbunny](https://boards.straightdope.com/u/missbunny)\ **Post date:** [September 30, 2004, 2:49pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/32 "2004-09-30T14:49:05Z")
> [@Qadgop the Mercotan](#): > > It’s the old 17/23 correlation. The Master spoke of it [here](http://www.straightdope.com/classics/a2_295.html). 😉 My secret has been revealed! You better watch out, QtM. “We” have our agents everywhere, even in that prison of yours. 😉 ---
**Author:** ![Qadgop\_the\_Mercotan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/qadgop_the_mercotan/32/83_2.png) [@Qadgop\_the\_Mercotan](https://boards.straightdope.com/u/Qadgop_the_Mercotan)\ **Post date:** [September 30, 2004, 3:45pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/33 "2004-09-30T15:45:10Z")
> [@missbunny](#): > > My secret has been revealed! > > You better watch out, QtM. “We” have our agents everywhere, even in that prison of yours. 😉 Yeah, I met one of your _agents_ earlier this week. I removed two of his toenails! He’s now seen the error of his ways. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [September 30, 2004, 11:06pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/34 "2004-09-30T23:06:19Z")
> [@Cabbage](#): > > **vanilla** , the chances of that happening are 0.000000000000000099671433849300578506753494359707 %. To be honest, I don’t believe you (unless your church has some strange policy, like not accepting new members if they have the same birthday as an already existing member). Maybe you should check the directory again. I dunno, one-in-a-quadrillion events do happen, like forming a lasting healthy romantic relationship with someone you met at a dance club. Just kidding. Barring a specific no-matching-birthday policy, and even accounting for some possible bias (i.e. babies in that particular town who are born during certain months have greater chances of dying in infancy, i.e. in harsh winter conditions), it’s much more likely that there is a data error somewhere. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [September 30, 2004, 11:11pm UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/35 "2004-09-30T23:11:13Z")
Whoops! If babies during certain months are more likely to die, than the odds are even _longer_. The kind of bias that might spread out the birthdays of a population could be from there being only one local obstetrician who uses various medical methods to delay or induce labour in his patients to make it unlikely he’ll ever have to deliver two babies in one day, plus he doesn’t work Mondays, wednesdays of Saturdays, or some damn thing. ---
**Author:** ![Faldage](https://avatars.discourse-cdn.com/v4/letter/f/f4b2a3/32.png) [@Faldage](https://boards.straightdope.com/u/Faldage)\ **Post date:** [October 1, 2004, 12:44am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/36 "2004-10-01T00:44:14Z")
Just a data point or three. I am in a group of 42 people with three pairs of same month/date birthdays. ---
**Author:** ![Fuji\_Kitakyusho](https://avatars.discourse-cdn.com/v4/letter/f/f0a364/32.png) [@Fuji\_Kitakyusho](https://boards.straightdope.com/u/Fuji_Kitakyusho)\ **Post date:** [October 1, 2004, 12:52am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/37 "2004-10-01T00:52:26Z")
My boss and I (the only two people in our company) discovered after working together for six months that we were both born on October 1. What are the odds? ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [October 1, 2004, 12:56am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/38 "2004-10-01T00:56:31Z")
> [@Fuji Kitakyusho](#): > > My boss and I (the only two people in our company) discovered after working together for six months that we were both born on October 1. > > What are the odds? One in 365, assuming the key element is that you have the same birthday, not that it’s Oct. 1 in particular. ---
**Author:** ![Punoqllads](https://avatars.discourse-cdn.com/v4/letter/p/d2c977/32.png) [@Punoqllads](https://boards.straightdope.com/u/Punoqllads)\ **Post date:** [October 1, 2004, 2:09am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/39 "2004-10-01T02:09:40Z")
> [@Fuji Kitakyusho](#): > > My boss and I (the only two people in our company) discovered after working together for six months that we were both born on October 1. > > What are the odds? Technically, 100%. ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [October 1, 2004, 3:17am UTC](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675/40 "2004-10-01T03:17:28Z")
> [@Bryan Ekers](#): > > One in 365, assuming the key element is that you have the same birthday, not that it’s Oct. 1 in particular. What if the Oct. 1 part is important? Before **Fuji** told us anything, the probability that he had a birthday of Oct. 1 was 1/365. The probability that his boss did was 1/365. The probability of both of these (1/365)^2 = 1/133,225 = 7.51 \* 10^-6 In laymen’s terms: Very small. [Previous page](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675.md?page=1) [Next page](https://boards.straightdope.com/t/chances-of-2-people-sharing-a-birthday-50/266675.md?page=3)