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

[Anonymous]

Regarding significant dates, coincidence, and probability, has anyone tried the exercise where you have approximately 30 people in a room, take down each of their birthdays, then look to see how many match? Most people think that with 30 people in a room and 365 days in a year that the odds would be pretty low. Due to some statistical quirks the odds are far higher than you'd think. Maybe some stats guru out there can explain this better.

 

[harlequin2005]

I think, at the risk of flippancy, we're getting into Pratchett Law territory:-

"One in a million chances happen nine times out of ten"



8¬)

 

[rynner2]

...has anyone tried the exercise where you have approximately 30 people in a room, take down each of their birthdays, then look to see how many match? Most people think that with 30 people in a room and 365 days in a year that the odds would be pretty low. Due to some statistical quirks the odds are far higher than you'd think. Maybe some stats guru out there can explain this better.

That question was in fact covered in an OU maths course I did. I'll have to look up the exact details. (If I try it off the top of my head I'll probably make a monkey of myself!)

 

[mikelegs]

I'm gonna just go ahead and make a monkey out of myself. Feel free to correct me and argue with me and make fun of me wherever I go wrong.

1 person's chance of having a b-day on a given day = 1/365

chance of 2 ppl having the same b-day = 1/365 (if this doesn't make sense, consider you have 364 chances of not having my bday)

add a person, and the chance of 2/3 ppl having same b-day = 2/365

as you add people, the chance of 2 ppl having the same b-day in any group of n is n-1/365.

Then take sociological factors into account (ie. certain seasons of the year more babies are made), and you can reduce the denominator to the point where a group of 30 has a pretty good shot at two of the same bday.

 

[rynner2]

Common Birthdays

This is a case where it is easier to calculate the case of something Not happening, and then invert it. I think the maths go like this:

First person has a birthday sometime: the chance of the second person having a different birthday is 364/365. The chance of a third person having a different birthday from the first two is 363/365. And so on. The chance of the Nth person having a different birthday from all the others so far is (366-N)/365.

With me so far?

So the chances of N persons ALL having different birthdays is the product of all these probabilities. Now it may come as a shock to those who think that computers can do anything that if you try this on a calculator or even a computer maths program, you will probably get an 'Overflow' message, meaning the numbers are too big to be handled to the required precision!! (It can be done, with more care, however.)

But what we have is a number less than one being multiplied by a number slightly smaller, being multiplied by a number even smaller, and so on. Soon the result is less than a half, meaning that the probability of the N people having different birthdays is less than 50-50. This implies that at least two of them have the same birthday. This occurs for (I'm not sure of the exact number) N = 30 (maybe less).

I bet DD wished now he'd never asked!

 

[SoundDust]

How about the millions who share those birthdays

I share a birthday with 2 other people in my work group - and theres 2 others with the same birthday on the same contract as us within the same building

 

[rynner2]

I share a birthday with 2 other people in my work group - and theres 2 others with the same birthday on the same contract as us within the same building

I recently created a gaph showing the probability that at least 2 people in a group have the same birthday, for groups up to 50 people (above that, it's a near certainty!)

I would attach it here, except that Attachments aren't working...

 

[DerekH16]

I recently created a gaph showing the probability that at least 2 people in a group have the same birthday, for groups up to 50 people (above that, it's a near certainty!)

I recall an anecdote about a house party (posh do!) consisting of something like 21 people where the maths professor said that, in a group of 22, 2 peeps would (probably, i.e. greater than evens chance) have the same birthday. None of them shared a birthday. He was slightly embarassed, but pointed out that 22 was the 'magic' number, not 21.

Later, the maid who'd been in the room at the same time (making room occupancy=22) mentioned that she had the same birthday as one of the guests, but was too shy to say.

QED.

 

[Jerry_B]

That's odd - I've never met anyone who shares the same birthday as me (may 13th).


Of course, living in a small cave off the coast of Switzerland doesn't help.

 

[rynner2]

To be precise, Derek, the number should be 23 - then the probablity is 50.7%, ie, just better than evens. Then the graph rises steeply as you add more people - for 50 people the probablility is about 97%.

Which means about a 3% chance that 50 people could all have different birthdays.

 

[Anonymous]

To be precise, Derek, the number should be 23 - then the probablity is 50.7%, ie, just better than evens. Then the graph rises steeply as you add more people - for 50 people the probablility is about 97%.

Which means about a 3% chance that 50 people could all have different birthdays.

There's that darned 23 again!

sureshot

 

[evilsprout]

That's odd - I've never met anyone who shares the same birthday as me (may 13th).

It's my old flatmate's birthday if that's any consolation.

 

[DerekH16]

To be precise, Derek, the number should be 23

I was almost right .... story of my life ......

 

[kiel_d]

I share a birthday with carole, it would seem. 5th May.

I've always found a lot of people with this birthday at school, college, work, family/friends, or is it that i just pick up on that day more as it has significance to me?

Is there any data showing the popularity of birthdays (ie more people born on june 4th than november 26th) or are the births roughly spread out through the year?

--kiel--

 

[gattino]

No. The odds against any GIVEN individual having a particular birthday would be 364 to 1. The odds against two specified individuals would be...er..either 2X 364 or ..um..is it 364x364 - 1; 3 specific inividuals would increases the odds proportionately in the same way.


In other words though the odds for each of them are the same the odds for all of them collectively multiply.


Probability theory is completely meaningless in the whole topic of unlikely events - it tells you nothing about whether a thing will or should or even could happen, whether for good or bad. It simply tells you to what degree, based on past experience or limited options, you can RELY on a thing happening. They don't say whether it can or can't, will or won't....only how silly or reasonable you are to EXPECT a particular outcome.

The odds against any one of us winning hte lottery are many millions to one. This has absolutely no detrimental effect on the fact that the lottery is won..by several people...twice a week! The odds for those people were no different than they are for the rest of us - astronomical - they still win.

 

[rynner2]

The chance of one specified individual having the same birthday as you is 1 in 365. The chance of two specified people having the same birthday as you is 1 in 365^2, ie, 1 in 133,225.

There are other posts on birthday probabilities earlier in this thread ...

Incidentally Sep 3rd is my daughter's birthday too, and the date France and UK declared war on Nazi Germany...

 

[rynner2]

BTW, here's the graph I mentioned earlier. Along the bottom is the number of people in a group, and the blue line shows the probability (in the range 0 to 1) that at least 2 of the group members share a birthday.

(The red line shows the probability that none of them share a birthday.)

 

[escargot]

A childhood friend of mine was born on the same day as I was. We lost touch until about a month ago when she joined my gym.

Turns out that her auntie lived next door to me until her recent death and I'd seen my old mate at the funeral without recognising her.

Maaad.

 

[rynner2]

It occured to me that the maths behind the graph I offered earlier should give an answer to Jaygordon's situation. Him, his brother, and his cousin form a group of 3, and the graph maths gives a probability of 0.0082 - which is over 100 times greater than the figure of 1 in 133,225 I gave above! :eek!!!!:

But then I realised the graph maths gives the probability of at least two of the group having the same birthday, not all three.

So with 3 people, A, B, and C, you can have A=B, or B=C, or C=A, or A=B=C (where '=' means 'has same birthday as'), which obviously is much more probable than than just A=B=C alone.

It just shows how careful you have to be with statistics!


(PS: The graph was made using Mathcad - I can send a copy of the Mathcad file to anyone interested in the details. Just PM me.)

 

[brianellwood]

Don't understand probability calculations but was once told that if you stand up on a double-decker bus and shout who has a b'day today at least two or more people will hold their hands up. Is this a probability?

 

[rynner2]

Don't understand probability calculations but was once told that if you stand up on a double-decker bus and shout who has a b'day today at least two or more people will hold their hands up. Is this a probability?

I don't think so.

This problem made me think, but I finally got my old brain into gear:

It's actually easier to first calculate the probablity of NONE of them having their birthday on the given day.
For each person, the probability is 364/365 that today is NOT the person's birthday. For N people, the probability that today is not the birthday of any of them is (364/365)^N.

As N increases, this figure drops slowly from almost 1, only reaching 0.5 when N=253. So you'd need 253 people on the bus to have odds of 50:50 on finding at least one person whose birthday is today! A pretty big bus, so I think the problem was mis-remembered: on a sensible size bus with 23 passengers, there is a 50:50 chance that two of them will share a birthday, but it would probably not be today!

A lot of statistics is counter-intuitive, so it might seem surprising that even with 365 people on the bus, the probablity of there being at least one person whose birthday is today is still only 0.633. (There could well be other shared birthdays, but not necessarily today.)

I thought about calculating the chances of at least two people having a birthday today, but then my brain gave up! I'll dig out my OU stuff and try again tomorrow.


Meanwhile, here's a story about a new view of evolution Cancer Selection, which was inspired by a remarkable coincidence:

Happily for Graham, Leroi had the forebearance to judge the work on its merits. "When I'd originally read Graham's book, I thought there was something in it. But I forgot it," he admits. Then he moved to the UK and started working with another evolutionary biologist, Austin Burt. "I can't remember whether he was in my office or I was in his, but we looked on each other's bookshelves and said, 'Gosh, Cancer Selection , you've got it too'."

It turned out that Burt had also picked up a remaindered copy of the volume in Moe's Bookshop, Berkeley, while in California as a postdoc.

An extraordinary chain of coincidences that began with two postdoc biologists buying the same rare book on opposite sides of America has now brought them together in London with a third colleague, Vassiliki Koufopanou, to pen their own thoughts on cancer.

 

[rynner2]

The WMN today has an Obit about a woman who died on Monday aged eleventy one, but I can't find it online.

However, I found an article about her last birthday here: http://tinyurl.com/od6jv

But why (I hear you cry), are you posting this here instead of on RIP or Growing Old?

Read on! 8)

Former suffragette becomes Britain's oldest woman
By Auslan Cramb, Scottish Correspondent
Last Updated: 2:11am BST 04/08/2006

Porridge for breakfast and a teetotal regime are the secret of a long life, says Britain's "new" oldest woman.

Annie Knight, a former suffragette who has lived in three centuries, inherited the title after the death this week of 111-year-old Emmeline Brice at a nursing home in Leighton Buzzard, Beds.

Mrs Knight celebrated her 111th birthday in June with a cake and a cup of tea at her home at the Royal Cornhill Hospital, Aberdeen, where she learned of her new position in the record books yesterday.

Her son Bill, 85, said: "Reaching 111 is quite remarkable. The nurses who look after her put it down to the porridge. She can't function without a bowl of it every morning.

"This is something she never, ever expected to happen. She lived for the moment. It's quite remarkable, even if she doesn't think it is all that great an achievement. "

Mrs Knight was born in Glasgow in 1895, while Queen Victoria was on the throne, and moved to Aberdeen when her father was given a job at an engineering plant.

She was six when the first radio transmission was received, 10 when Albert Einstein published the theory of relativity and 30 when television was invented.

She worked in a department store while studying from home for a degree from the London School of Music and later became a piano teacher.

She met her husband, William, during the First World War while he was on leave from the Royal Engineers and they had two sons. Her younger son Harold died two years ago, aged 81.

Mr Knight said his mother held strong political views, was an outspoken advocate of women's rights, attended and organised suffragette meetings in Aberdeen and became a staunch Scottish nationalist.

"She was hardly ever at home in the evenings," he said. "She was always away at a demonstration or campaign meeting. She relished being a part of the suffragettes, but she was never arrested or in trouble with the authorities. That kind of thing was only happening down in London. She could be quite argumentative when challenged but she wanted to make things better for all women."

Mr Knight, who has put her name forward to Guinness World Records as the oldest woman in Britain, said she had never drunk alcohol and sweets were her only vice.

Coincidentally, the country's oldest woman now shares her birthday - June 6 - with the country's oldest man, Henry Allingham, 110, from Eastbourne, Sussex, one of about 20 surviving servicemen who fought in the First World War. :shock:

I leave it to statisticians to work out the odds of two people with the same birthday living to 110+!

 

[rynner2]

Cambridge don launches bizarre study into coincidence
By Jo Macfarlane
Last updated at 12:31 AM on 15th January 2012

A Cambridge don is appealing to the public for tales of striking coincidences – so he can analyse just how strange they really are.
Professor David Spiegelhalter hopes the exercise will help him calculate the odds of such peculiar events occurring.

The professor of public understanding of risk at Cambridge University told Radio 4’s Today programme: ‘I usually deal with risk stories, the arbitrary accidents and illnesses that befall us.
‘This time we’re looking at the upside of the way chance works, these strange things that happen to us when we say, "What are the odds of that?" ...

Prof Spiegelhalter also explained that sharing a birth date with several other family members is not as surprising as it might appear.
In fact, he says there is a one in 35,000 chance that a child will share a birthday with a parent and grandparent – better odds than winning the lottery. ...

Another reported: ‘I have two unrelated godsons, for whom I was chosen a few years apart.
‘Both are called Edward. Both were born on October 4 (four years apart). Both their fathers are called Graham.’ ...

www.understandinguncertainty.org/coincidences

Read more: http://www.dailymail.co.uk/news/article ... z1jXPOT9Cj

 

[rynner2]

I've had a tune going round my head, and I thought, "Who sang that?" I remembered the name of the entertainer, but I haven't heard of him for a few years, so I checked on Wiki to see if perhaps he'd kicked the bucket.

Apparently not. And what's more, he was born on the same day I was! :shock:

Now same day and month is just a 1/365 chance, but how to factor in the year as well? Take people born in a 100 year span, from 1914 to now, and that will include most of the people alive now. (It'll miss those aged 100+, and include quite a few who've already died, but it'll do as a round figure estimate.)
So the chance that a random birthday is exactly the same as your own is 1/36,500 (or just under 3 in a hundred thousand).

The things that come from a 'stuck tune', eh! 8)

 

[rynner2]

So what was the tune and who was the performer?

I'm not telling you that! As soon as you've got my DOB you'll be googling away to find my N.I. number, name, address, bank account details and inside leg measurement!

(But I'll give you a clue - it wasn't Cliff! )

 

[rynner2]

I've had a tune going round my head, and I thought, "Who sang that?" I remembered the name of the entertainer, but I haven't heard of him for a few years, so I checked on Wiki to see if perhaps he'd kicked the bucket.

Apparently not. And what's more, he was born on the same day I was! :shock:

Now same day and month is just a 1/365 chance, but how to factor in the year as well? Take people born in a 100 year span, from 1914 to now, and that will include most of the people alive now. (It'll miss those aged 100+, and include quite a few who've already died, but it'll do as a round figure estimate.)
So the chance that a random birthday is exactly the same as your own is 1/36,500 (or just under 3 in a hundred thousand).

Here's a chap who makes a hobby out of searching out his Time Twins:

‘Time twins’ prevent man’s mid-life crisis

AN avid traveller from Lancing is attempting to seek out 40 ‘time twins’ from across the globe before he reaches his 40th birthday.
Richard Avis, 38, decided on meeting a diverse range of people who share his date of birth, rather than ‘slumping into a mid-life crisis’.

He said: “I reached a point in my life in my late 30s where I started to compare my life with other people. Was I successful? What does success look like? Was I young, middle-aged, or old?

“As I, and the rest of the team, enjoy travelling and are fascinated by global cultural diversity, this seemed a perfect opportunity to develop those interests.”

So far Richard and his team have met a Dutch National Body Building and Model Physique champion, an Irish novelist and the mayor of an Italian town, Richard’s highlight so far.

http://www.worthingherald.co.uk/what-s- ... -1-5641810

He also has a website:

Time Twins

I’m travelling the world, meeting people born on the same day as me. Are you one of these ‘Time Twins’?

Synopsis

This is the story of one man’s journey around the world to meet people born
on exactly the same day as him: his Time Twins.

I was born on 1st December 1974 in Dumfries, Scotland. With my thirties
slipping away, I kept asking himself [sic]: what have I done with my time? What could I have done if things had turned out differently? But I realised he wasn’t alone; all over the world there are people born on exactly the same day as him.

Three of his old friends, Geoff (historian), Simon (internet entrepreneur), and Stuart (seasoned traveller), challenged me to meet 40 Time Twins of different nationalities by the time I reach 40 years old. They set off on a shoestring budget, squeezing the project into their spare time and searching for a publisher.

The Time Twin Project celebrates the richness of human life: with the same number of days on the planet, what kinds of lives have these people lived? What are their greatest achievements? How have they been affected by triumph and tragedy? Have they had their defining moment, or is that still to come? Are they successful – and how is this judged in different cultures? Does the concept of age change from country to country?

Although all the Time Twins share the same date of birth, they are diverse in ethnicity, gender, religion, occupation and social background. Some are famous; most are not. As well as providing fascinating insights into their lives, the Time Twins act as windows on their countries, cultures, and the events that have shaped their lives.

http://richardavis.com/01121974-2/

Diverse they are, and it's only coincidence that links these 'Time Twins' together - unless you're into astrology! I don't really want to get into that myself, but an astrological viewpoint might be interesting... 8)

 

[gellatly68]

I've had a tune going round my head, and I thought, "Who sang that?" I remembered the name of the entertainer, but I haven't heard of him for a few years, so I checked on Wiki to see if perhaps he'd kicked the bucket.

Apparently not. And what's more, he was born on the same day I was! :shock:

Now same day and month is just a 1/365 chance, but how to factor in the year as well? Take people born in a 100 year span, from 1914 to now, and that will include most of the people alive now. (It'll miss those aged 100+, and include quite a few who've already died, but it'll do as a round figure estimate.)
So the chance that a random birthday is exactly the same as your own is 1/36,500 (or just under 3 in a hundred thousand).

How about this one?
I came back to my house on my fortieth birthday after a day out with the (now ex-) missus and the kids, and noticed that our next door neighbour had a 'happy 40th!!' banner and balloons outside HER house. As we went by, she came to the door, and I said something along the lines of 'thanks for remembering my birthday'. She looked confused, and said 'It's your birthday? It's also X's birthday!', X being her partner, who had moved in with her about a year before.
It turned out that not only did we share the same birthday, we were born within a few minutes of each other!

 

[Mythopoeika]

It turned out that not only did we share the same birthday, we were born within a few minutes of each other!

Are you twins without realising it?

 

[rynner2]

Big footie match today in the Premier league, Liverpool v. Chelsea.

But this is not exactly a footie statistic as such - it seems the two managers have the same birthday,
26 January!
José Mourinho, Chelsea, 1963
Brendan Rodgers, Liverpool, 1973.

There are only 20 teams in the English PL.

So what are the chances of these two managers contesting a top-of-the-table match this late in the season?

Chelsea won, so are now only two points behind Liverpool at the top of the table.

 

[Peripart]

Big footie match today in the Premier league, Liverpool v. Chelsea.

But this is not exactly a footie statistic as such - it seems the two managers have the same birthday,
26 January!
José Mourinho, Chelsea, 1963
Brendan Rodgers, Liverpool, 1973.

There are only 20 teams in the English PL.

So what are the chances of these two managers contesting a top-of-the-table match this late in the season?

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'd therefore lay odds that, in at least 2 of the 3 leagues below the Prem, there are mangers sharing birthdays. Someone else can check, though...