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Shared Birthdays Among Any Group Of People (Probability; Odds)

Peripart said:
Statistics can be a very counter-intuitive branch of mathematics. It's slightly unlikely that 2 PL managers (out of 20) share the same birthday, but for any given group of people, you only need 24 or 25 (I forget which) for there to be a greater than 50% chance that at least one pair share a birthday.
I know that, but I was not considering random pairs, but one particular pair, involved in one specific, top-of-the-table, match. The match selects the managers, so there are only two to consider. Therefore it seems to me the chance must be about 1/365. Factor in the chance of the two top teams playing each other late in the season, and the chance must be even smaller!


The more general Birthday problem is discussed on Wiki:
https://en.wikipedia.org/wiki/Birthday_problem

(23 people are needed for a better than 50% chance.)
 
rynner2 said:
Peripart said:
Statistics can be a very counter-intuitive branch of mathematics. It's slightly unlikely that 2 PL managers (out of 20) share the same birthday, but for any given group of people, you only need 24 or 25 (I forget which) for there to be a greater than 50% chance that at least one pair share a birthday.
I know that, but I was not considering random pairs, but one particular pair, involved in one specific, top-of-the-table, match. The match selects the managers, so there are only two to consider. Therefore it seems to me the chance must be about 1/365. Factor in the chance of the two top teams playing each other late in the season, and the chance must be even smaller!

The more general Birthday problem is discussed on Wiki:
https://en.wikipedia.org/wiki/Birthday_problem

(23 people are needed for a better than 50% chance.)
An article discussing this (and football, again!) is this:

The birthday paradox at the World Cup
By James Fletcher, More or less, BBC Radio 4

It's puzzling but true that in any group of 23 people there is a 50% chance that two share a birthday. At the World Cup in Brazil there are 32 squads, each of 23 people... so do they demonstrate the truth of this mathematical axiom?

...

"The birthday paradox is one of maths' greatest hits," says Alex Bellos, author of Alex Through the Looking Glass: How Life Reflects Numbers and Numbers Reflect Life.
"It's something you can say in one line which gives you this 'wow'!"

In its most famous formulation, the birthday paradox says that you only need a group of 23 people for there to be a greater than 50% chance that two of them share the same birthday.
(For lovers of detail, we should be clear that by birthday we mean day and month, not year.)

Bellos points out that the birthday paradox isn't a logical paradox - there's nothing self-contradictory about it, it's just unexpected.

...

At the 2010 World Cup, Algeria's squad actually had three players whose birthday fell on the same day, 5 December. No squad achieves that this time round, but 2014 might have the rarest shared birthday of all.

Imagine this scenario: Germany come top pool of G, and Algeria come second in pool H. On 30 June the two teams would then face each other in the round of 16.

If it happens, watch out for a knowing glance from the bench or an extra warm handshake between Benedikt Howedes of Germany and Saphir Taider of Algeria - they share the pain of celebrating their real birthday just once every four years, because both were born on 29 February. 8)

...

And some interesting stats about the distribution of World Cup Birthdays (see article for discussion):

For the 2014 World Cup players, the four months with the most birthdays are January (71), February (77), March (68 ) and May (72). These are all above the 61 birthdays a month you'd expect if they were evenly distributed.
And the months with the fewest birthdays all come in the second half of the year: August (57), October (46), November (49) and December (51).
The 2010 data show the same thing - above average early in the year, below average towards the end.

This is just a quick look at the figures and not a definitive analysis, but it at least suggests that the theory that World Cup players tend to be born in the first half of the year isn't dead and buried.

(So no wonder I didn't get picked for England!) :(

http://www.bbc.co.uk/news/magazine-27835311
 
I was helping out on the IT Helpdesk today - processing emails from customers who have typically forgotten or mistyped their passwords and need some software maintenance to unlock their accounts, reset passwords or user names etc.
Once I've confirmed a customer's identity, which includes checking date of birth and NI number, I call up their record to confirm its status - active, disabled, suspended etc.
My first customer today had the same birthday as me. I managed to resolve his technical issue quite easily and mentioned that we shared a birthday and wished him a happy birthday for a couple of weeks ago.
There's a coincidence, I thought.
Onto my second customer and, you guessed it, also the same birthday as me.
Now that is just plain weird!

Over the (very long) day, I processed another 40 or so customer queries, with no other DOBs coinciding with mine.
Those first two of the day gave me quite an unreal feeling though.
 
I was helping out on the IT Helpdesk today - processing emails from customers who have typically forgotten or mistyped their passwords and need some software maintenance to unlock their accounts, reset passwords or user names etc.
Once I've confirmed a customer's identity, which includes checking date of birth and NI number, I call up their record to confirm its status - active, disabled, suspended etc.
My first customer today had the same birthday as me. I managed to resolve his technical issue quite easily and mentioned that we shared a birthday and wished him a happy birthday for a couple of weeks ago.
There's a coincidence, I thought.
Onto my second customer and, you guessed it, also the same birthday as me.
Now that is just plain weird!

Over the (very long) day, I processed another 40 or so customer queries, with no other DOBs coinciding with mine.
Those first two of the day gave me quite an unreal feeling though.

Not as weird as you might think. You only have to have a group of 23 people to ensure a 50:50 chance of two of them having the same birthday. For (about) 42 people, the odds are approximately 9 in 10.

Birthday_Paradox.jpg

https://en.m.wikipedia.org/wiki/Birthday_problem

maximus otter
 
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Not as weird as you might think. You only have to have a group of 23 people to ensure a 50:50 chance of two of them having the same birthday. For (about) 42 people, the odds are approximately 9 in 10. ...

That's if you compare DOBs across a group of people though.
The odds on the first record matching my birthday is surely 365 to 1?

The odds on the very next record also matching my birthday is 365 x 365 or 133,225 to 1, which is pretty high.
Since yesterday morning's coincidence, I've processed around 50 helpdesk emails and my DOB has not occurred.
 
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That's if you compare DOBs across a group of people though.
The odds on the first record matching my birthday is surely 365 to 1?

The odds on the very next record also matching my birthday is 365 x 365 or 133,225 to 1, which is pretty high.

That's not how "random" works.

In a group of 42 people, one of them being yourself, you found two matches. Whether the match was the first or the forty-first is irrelevant.

maximus otter
 
Another set of related coincidences came to my mind on a bike ride earlier today.

Roughly speaking, the chance of a randomly chosen person having the same birthday as me is 1/365. Thus, if I check the birthdays of 365 people, it is likely, although not certain, that one will have the same birthday as me. (Talking here about day/month but not year as well.)

I spent over 35 years in an insurance job in which I had to check the date of birth of at least one person on every case that I saw: always the Policyholder and often the driver of a vehicle too. I checked anything from 5 people a day up to 30 or more.

I never once came a cross a customer with the same birthday as me. I would certainly have noticed because I have that sort of mind: it's an affliction!

I had to check their names too, obviously, and I never once came across someone with the same forename and surname as me. Towards the end of my time there, though, I became aware of a person in another company in the group who shared my name, which caused problems with email.

However, after knowing a fellow Morris dance teacher for many years, it came out in the conversation that we shared a birthday. He is 30 years older than me to the day.

My first wife and I were school mates before we were a couple. Within one school year group of around 100 people, about 5 had the same birthday as her (6th May) and 2 of those were in our close friendship group.

When my wife left school, she started a job in a small laboratory in Nottingham and in that little group of a dozen people, one had the same birthday as her: 6th May.

After we separated, I met got together else. She had the same birthday as one of my brothers (6th January).

Even more of a coincidence: one of her 2 daughters, Charlotte, had the same birthday as my brother, Charles.

Years later, I met my future 2nd wife. It came out in the conversation that she had shared a birthday with her late husband. We are now married and I have "inherited" 2 fine sons, one of whom has a birthday, 6th January: the same as my brother and my ex.

The bizarre thing is how "rare" my birthday seems to be in a massive sample of people whose details I have had to check, and yet how "common" 6th May and 6th January seem to be in the small sample of people I know personally.
 
I think there are 'popular' times of year to be born, so the odds might not be quite 1/365. For example, people generally try to avoid having a child born in August, as they will be the youngest in the school year, which can lead to problems. So those planning their family will be more likely to try to aim to have children around September and October. Less creeping up to Christmas, but starting again in February/March.

So there will be 'clusters' of birthdays. When my middle daughter (born 06 June) started school, her entire class were born within three weeks of each other. (Admittedly, small class at local village school, so probably ten children).
 
I think there are 'popular' times of year to be born, so the odds might not be quite 1/365. For example, people generally try to avoid having a child born in August, as they will be the youngest in the school year, which can lead to problems. So those planning their family will be more likely to try to aim to have children around September and October. Less creeping up to Christmas, but starting again in February/March.

So there will be 'clusters' of birthdays. When my middle daughter (born 06 June) started school, her entire class were born within three weeks of each other. (Admittedly, small class at local village school, so probably ten children).
I think this concept is more of a modern thing, it used to be that a lot of babies were born in the late summer months up to late autumn as nine months before this it was cold wet and dark of an evening and couples would get jiggy to pass the time and keep warm :D
 
I think this concept is more of a modern thing, it used to be that a lot of babies were born in the late summer months up to late autumn as nine months before this it was cold wet and dark of an evening and couples would get jiggy to pass the time and keep warm :D
This actual timing is more modern, but there were always birth 'clusters', going back to the times when it was safer to have a baby in the spring, to be as mature as possible to survive the winter.
 
I think this concept is more of a modern thing, it used to be that a lot of babies were born in the late summer months up to late autumn as nine months before this it was cold wet and dark of an evening and couples would get jiggy to pass the time and keep warm :D

In rural societies June weddings were considered appropriate because a young healthy couple would hope to have their first baby in the following spring. This gave them six months of warm weather during the child's first year.
 
This actual timing is more modern, but there were always birth 'clusters', going back to the times when it was safer to have a baby in the spring, to be as mature as possible to survive the winter.
Yeah i meant the thing about not wanting your kid to start school 11 months later than every one else, coincidentally my brother was born on june 4th, dad june 7th and mom june 8th, me feb 12th lol
 
Yeah i meant the thing about not wanting your kid to start school 11 months later than every one else, coincidentally my brother was born on june 4th, dad june 7th and mom june 8th, me feb 12th lol
Yes, I used the 'Autumn birth' thing to illustrate that there are, and have always been, birth clusters. It's not THAT recent a concept, although actually planning your conception so as not to have a child who is the youngest in the school year is fairly recent, that is because schools used to have intakes throughout the year, rather than everyone starting in September.
 
I know quite a few people with birthdays 15th - 25th November.
Coincidence?
No.
It's 9 months after Valentines.
There you go: as my birthday is in that range, it is all the more surprising that in over 35 years of checking customers' details, I never once found one with my exact birthday, and I know only one person socially with it.

(I'm not giving my exact birthday here out of caution: identity theft and fraud work by collecting small amounts of information like that separately and compiling them.)
 
There you go: as my birthday is in that range, it is all the more surprising that in over 35 years of checking customers' details, I never once found one with my exact birthday, and I know only one person socially with it.

(I'm not giving my exact birthday here out of caution: identity theft and fraud work by collecting small amounts of information like that separately and compiling them.)

In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.


The computed probability of at least two people sharing a birthday versus the number of people

https://en.m.wikipedia.org/wiki/Birthday_problem

maximus otter
 
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In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.


The computed probability of at least two people sharing a birthday versus the number of people

https://en.m.wikipedia.org/wiki/Birthday_problem

maximus otter
I think the birthday paradox was what I had in mind.

Although date of birth seems to be random, nature has preferences. It's like the thing with time of birth, most young are born during the hours of darkness (although, nowadays, not necessarily human babies).

Edited for clarity because, quite often, even I don't know what I'm on about.
 
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.


The computed probability of at least two people sharing a birthday versus the number of people

https://en.m.wikipedia.org/wiki/Birthday_problem

maximus otter
You beat me to it, Max. This is something we use in mentalism. People expect it to be 1/365 but a group of 70 or 80 will be enough for a "coincidence".
 
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.

By the pigeonhole principle, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (excluding February 29) is equally probable for a birthday.


The computed probability of at least two people sharing a birthday versus the number of people

https://en.m.wikipedia.org/wiki/Birthday_problem

maximus otter

There are two different situations here:

Mike Fule's original coincidence - actually a 'no-incidence'
Mike Fule said:
I spent over 35 years in an insurance job in which I had to check the date of birth of at least one person on every case that I saw: always the Policyholder and often the driver of a vehicle too. I checked anything from 5 people a day up to 30 or more.

I never once came a cross a customer with the same birthday as me. I would certainly have noticed because I have that sort of mind: it's an affliction!

was asking the chances of matching a particular birthday, his own. He said this is ~ 1/365, so we can take it that he wasn't born on 29 Feb.
If you do the sums, we get that you need 253 people to have a 50-50 chance of matching a particular birthday. This is probably much higher than most people's intuition, similar to how the figure of 23 for a 50-50 chance of any matching birthday is much lower than intuition.

Anyway to return Mike Fule's birthday uniqueness. If he saw an average of 12 birth dates a day that would be 60 a week and so approaching 250 a month. So we'd expect about a 50-50 chance of seeing his birthday each month. And to not see it ever would be like tossing a coin each month for 35 years and getting tails every time: that's astonishing!

oxo
 
My sister's birthday falls on the day between those of my brother-in-law and mother-in-law. It's an expensive month, considering my dad's birthday is a week later and my husband's niece's is a week before that cluster!
 
I
My sister's birthday falls on the day between those of my brother-in-law and mother-in-law. It's an expensive month, considering my dad's birthday is a week later and my husband's niece's is a week before that cluster!
Think i mentioned up thread, June is my nightmare month, i only buy b'day prezzies for my direct family but my brothers is the 4th, dads the 7th and moms the 8th :oops:
 
I

Think i mentioned up thread, June is my nightmare month, i only buy b'day prezzies for my direct family but my brothers is the 4th, dads the 7th and moms the 8th :oops:

October is our month.

We have 10 family birthdays in the first two weeks.
 
That's a lot of Libras!
 
Oooh ooh! This thread reminds me of a nicely odd occurrence I had when travelling on a local bus about 10-12 years ago.

I was travelling with my mum on the bus back from the local large town to our respective homes along the route and we were talking about birthdays. The bus was packed out, and so maybe we were chatting a little more loudly than usual due to the noise level from all the passengers and the rattly rural bus (we get all the urban cast-offs down here in the deep south west!).

I remarked that in my 40-or-so-odd years I'd never met anyone with the same birthday as me and mentioned the date. The lady behind us (I recognised her slightly, she worked in a local library I used occasionally) tapped me on the shoulder and said, "that's my birthday" and I was stupidly delighted to finally meet someone else with the same birthday. Then the little girl sitting in front of us with her Gran turned around to tell me it was her birthday too! I had my passport with me for some official reason and she was as happy as me to meet two other unrelated people in the same place at the same time with that birthday.

Maybe someone can work out the odds of 3 people on a bus holding about 45 people sharing the same birthday?

When things like this happen it makes me irrationally happy :)
 
Having gone through the whole thread, there were two other people on the boards who shared my birthday! (Along with Tammy Wynette, Michael Palin and Karl Marx.). And I know two other people born on that date - one whom I knew at work, and another who is a cyber friend.
 
I met two strangers today who share my birthday - not just the date, but the year also!

We were all queuing for our first Covid jab, and when they asked for DOBs, the three of us parroted out the same numbers. We all became eligible on Monday (when it was opened up to 44 year olds) so I guess they must be sending the text invitations out in date batches and we booked at the same time.

Still, pretty funny coincidence. The fact that we all had shaved heads and were wearing blue jeans, black jackets, and black masks must have made us look like triplets.
 
I met two strangers today who share my birthday - not just the date, but the year also!

We were all queuing for our first Covid jab, and when they asked for DOBs, the three of us parroted out the same numbers. We all became eligible on Monday (when it was opened up to 44 year olds) so I guess they must be sending the text invitations out in date batches and we booked at the same time.

Still, pretty funny coincidence. The fact that we all had shaved heads and were wearing blue jeans, black jackets, and black masks must have made us look like triplets.
You sure you weren't in a hall of mirrors? :p
 
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