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-   -   The Birthday Paradox (https://www.cpfc.org/forums/showthread.php?t=273620)

Louis 11-01-2018 05:24 PM

The Birthday Paradox
 
Heard this on the radio recently ... How many people do you need in a room to have a 50% chance of two having the same birthday?

https://betterexplained.com/articles...thday-paradox/

hughff 11-01-2018 05:32 PM

Haven't opened the link but IIRC it's about 25-30. Then at about a 95% chance it's around 40

Of course to have a 100% chance you need at least 367 people - one for each day of the year plus one more.

hughff 11-01-2018 05:36 PM

Opened the link - a couple fewer than I thought. and 95% was 48.

Really cool piece of stats. Frequently used by Maths teachers to impress their classes.

ExiledStirling 11-01-2018 05:47 PM

Has anyone actually tested this out for real?

I get the logic but still struggle to see that if in reality if you grouped together a number of times 23 people that reality will match the logic used.

Funk Butter 13-01-2018 01:58 AM

Quote:

Originally Posted by ExiledStirling (Post 14047685)
Has anyone actually tested this out for real?

I get the logic but still struggle to see that if in reality if you grouped together a number of times 23 people that reality will match the logic used.

I actually just started learning Japanese here in Japan. At the entrance, we had about 80 people line up according to birthday. I would say there was about 7 or 8 that had the same birthday and two sets of three people with the same birthday.

I actually like the Monty Hall Problem. But it tends to be more relevant to Americans that have watched Let's Make a Deal.

ExiledStirling 13-01-2018 02:12 AM

Quote:

Originally Posted by Funk Butter (Post 14049965)
I actually just started learning Japanese here in Japan. At the entrance, we had about 80 people line up according to birthday. I would say there was about 7 or 8 that had the same birthday and two sets of three people with the same birthday.

Interesting and perhaps more than expected but if yiu are at a college could you randomly go and get 10 sets of 23 people and see whether you get 5 of the groups to have two people sharing the same birthday?

Report back tomorrow :)

eagles073 13-01-2018 02:17 AM

I was on a train with 10 friends on a day out, and not one of us had the same birth month, which i thought was kind of freaky.

hughff 13-01-2018 03:11 AM

Quote:

Originally Posted by ExiledStirling (Post 14047685)
Has anyone actually tested this out for real?

I get the logic but still struggle to see that if in reality if you grouped together a number of times 23 people that reality will match the logic used.

As I inferred above, a maths teacher at my school used to do it every year. It certainly works.

Hedgehog 13-01-2018 03:26 AM

I know a lot of BBS Members don't advertise their birthday, but out of 6,944 members I would think at least 25% would. (Just look at this thread for example).

That would be a data base of 1,736 known birthdays. Divide that by the magic 23 and you get 75 sub-sets.

My fuzzy logic is that would mean at least 150 BBS members would have a birthday today (a minimum of 2 per 23 sub-set), yet the forums page shows there are only 5.

Stick that in your pipe and smoke it!

Chris Finch 13-01-2018 04:09 AM

I worked in an office of 9 people before and 3 of us shared the same birthday.
About 20 years apart in age but unusual nonetheless.

hughff 13-01-2018 04:21 AM

Hedgehog, you should never get a job in statistics.

N Herts Eagle 13-01-2018 05:22 AM

Quote:

Originally Posted by Hedgehog (Post 14049984)
I know a lot of BBS Members don't advertise their birthday, but out of 6,944 members I would think at least 25% would. (Just look at this thread for example).

That would be a data base of 1,736 known birthdays. Divide that by the magic 23 and you get 75 sub-sets.

My fuzzy logic is that would mean at least 150 BBS members would have a birthday today (a minimum of 2 per 23 sub-set), yet the forums page shows there are only 5.

Stick that in your pipe and smoke it!

Fuzzy Logic.... so let me check 150 *365 = 1736 or 54750........ Ok stage further its 5 so possible that two subsets could be fine but that leaves the chances for 145 people to have the same birthday a little shorter

Hedgehog 13-01-2018 05:23 AM

Quote:

Originally Posted by hughff (Post 14050001)
Hedgehog, you should never get a job in statistics.


Very true! :-)

ceeby 13-01-2018 07:28 AM

Quote:

Originally Posted by hughff (Post 14047653)
Haven't opened the link but IIRC it's about 25-30. Then at about a 95% chance it's around 40

Of course to have a 100% chance you need at least 367 people - one for each day of the year plus one more.

Even a million people in the same room wouldn't give you a 100% chance (although it would be crowded :p )

Worksop Palace 13-01-2018 07:37 AM

Quote:

Originally Posted by hughff (Post 14047653)
Haven't opened the link but IIRC it's about 25-30. Then at about a 95% chance it's around 40

Of course to have a 100% chance you need at least 367 people - one for each day of the year plus one more.

Having 367 people in a room wouldn’t give you a 100% chance of matching your birthday

Edit - beaten to it !

Away 13-01-2018 07:51 AM

Quote:

Originally Posted by Worksop Palace (Post 14050088)
Having 367 people in a room wouldn’t give you a 100% chance of matching your birthday

Edit - beaten to it !


The original problem was any two the same, not someone else the same as you which is a) very different and b) the way we intuit the (wrong) answer.

Worksop Palace 13-01-2018 07:55 AM

Quote:

Originally Posted by Away (Post 14050108)
The original problem was any two the same, not someone else the same as you which is a) very different and b) the way we intuit the (wrong) answer.

That, my friend, is a fair and valid point

Finbar 19-02-2018 03:57 AM

Remember reading this at the time, World Cup squads are perfect as there are 23 players in each one, in the 2014 the number of teams with 2 or more players with the same birthday was indeed 50%, I'm the same as you I just can't believe it would actually work out but seemingly it does

Here is the article and the proof

www.bbc.com/news/magazine-27835311


Quote:

Originally Posted by ExiledStirling (Post 14047685)
Has anyone actually tested this out for real?

I get the logic but still struggle to see that if in reality if you grouped together a number of times 23 people that reality will match the logic used.


Louis 03-03-2018 04:28 PM

Quote:

Originally Posted by Finbar (Post 14121387)
Remember reading this at the time, World Cup squads are perfect as there are 23 players in each one, in the 2014 the number of teams with 2 or more players with the same birthday was indeed 50%, I'm the same as you I just can't believe it would actually work out but seemingly it does

Here is the article and the proof

www.bbc.com/news/magazine-27835311

Good article to illustrate and explain it

Funk Butter 01-07-2018 09:14 PM

Since I didn't see an article related to the birthday stats of this year's World Cup squads, I did it myself. Of the 32 teams, 16 have two players with the same birthday. Poland takes the title with 4 sets of players with the same birthday. (all different ages, though) Portugal has three sets of players and Morocco and Brazil have two sets of players with the same birthday.

Finbar 02-07-2018 12:12 AM

That is awesome work, exactly 50% :)

It seems incredible to have 4 on the same day. Like spinning 365 number roulette wheel 25 times and getting the same number 4 times. Though thinking of it like that I can see that it could be 50/50 to get 1 repetition in those 25 spins

CommercialStone 24-08-2018 11:15 AM

Quote:

Originally Posted by hughff (Post 14047653)
Haven't opened the link but IIRC it's about 25-30. Then at about a 95% chance it's around 40

Of course to have a 100% chance you need at least 367 people - one for each day of the year plus one more.

Still not 100% though.....

NorthernEagle80 24-08-2018 11:31 AM

Not totally relevant but my girlfriend shares a birthday with her Dad and I share one with my Nephew. I would have thought that would be pretty long odds. My Niece is also only 2 days from my Sister.

switchboard 24-08-2018 11:36 AM

Quote:

Originally Posted by ExiledStirling (Post 14047685)
Has anyone actually tested this out for real?

I get the logic but still struggle to see that if in reality if you grouped together a number of times 23 people that reality will match the logic used.

Can't we simply prove or disprove this with how many posters it takes to find someone who shares our birthday?

I'll start if anyone wants to join

24th May

Finbar 24-08-2018 11:41 AM

Well I think the World Cup squad link above proves it in real life quite well

Anyway, 3rd June

Funk Butter 24-08-2018 01:11 PM

Quote:

Originally Posted by CommercialStone (Post 14399621)
Still not 100% though.....

Are you using something other than the Gregorian calendar?

David of Kent 24-08-2018 01:15 PM

Our office has 32 people in it with 2 pairs of identical birthdays.

Away 24-08-2018 05:27 PM

Quote:

Originally Posted by Funk Butter (Post 14399763)
Are you using something other than the Gregorian calendar?


Didn't read the question properly.

palacemetros 24-08-2018 08:49 PM

Quote:

Originally Posted by Finbar (Post 14399651)
Well I think the World Cup squad link above proves it in real life quite well

Anyway, 3rd June

Mrs Palacemetros is 3rd June!

25th October

Funk Butter 25-08-2018 02:51 AM

For those of you going to the match tomorrow, here's something you can do while you wait for kickoff. (Btw, he mentions my birthday in the video. There has to be something like a .54% chance of that happening)


Funk Butter 29-05-2019 10:41 PM

Since we have another World Cup coming up, I decided to check out some birthdays. Of the 24 teams playing in the Women's World Cup coming up, 11 have players that share the same birthday. Brazil is the only country with more than one duplicate birthday with two. There are two Brazilians and two Chileans that were born on December 17th.

Throughout the whole tournament, there are three players born on 12/17/1993 and 10/2/1992. There are 28 other instances of two players having the same exact birthday (including year).

https://en.wikipedia.org/wiki/2019_F...rld_Cup_squads

Am Phibian 29-05-2019 10:51 PM

3 of us had the same birthday in junior school class and 2 in my senior school one. 45 boys and 4 of us born on the same day.

Funk Butter 30-05-2019 03:12 PM

For extra completeness, I checked out the birthdays for the squads in the U-20 World Cup. Of the 24 of those teams, 12 had players with the same birthday. Norway, Poland, Senegal and the US had two pairs of players with the same birthday while Portugal had three sets.

Funk Butter 11-06-2021 05:56 AM

Another tournament and I've checked to see how many teams have players with matching birthdays. This time, teams are allowed to select up to 26 players for the tourney. As a result, this tournament has 18 of the 24 teams with multiple players with the same birthday. North Macedonia and Poland have 4 sets of players with the same birthday. England and Turkey have 3 sets. In fact, there is one team that not only has three players that share the same birthday but those players all play for the same club team. Bit of trivia for you to guess.

Finbar 11-06-2021 06:11 AM

Top statting FB, still find this maths hard to believe

wedgetail 11-06-2021 07:44 AM

Humans have bad intuitions regarding statistics, on average.

EdMan 11-06-2021 07:49 AM

Quote:

Originally Posted by hughff (Post 14047653)
Haven't opened the link but IIRC it's about 25-30. Then at about a 95% chance it's around 40

Of course to have a 100% chance you need at least 367 people - one for each day of the year plus one more.

I'm not sure that having 367 people in a room guarantees that at least two of them will have the same birthday. :angel:

Wolfnipplechips 11-06-2021 08:08 AM

Quote:

Originally Posted by Funk Butter (Post 14316321)
Since I didn't see an article related to the birthday stats of this year's World Cup squads, I did it myself. Of the 32 teams, 16 have two players with the same birthday. Poland takes the title with 4 sets of players with the same birthday. (all different ages, though) Portugal has three sets of players and Morocco and Brazil have two sets of players with the same birthday.

In other news; the long winter nights must fly by. :):p

jf63 11-06-2021 11:12 PM

My wife has a sister born on her birthday 5 years later and another sister that shares my sisters birthday, if this helps

El Aguila 11-06-2021 11:29 PM

This thread is missing Antoine Griezmann.

KYLIE MINEAGLE 12-06-2021 12:23 AM

Quote:

Originally Posted by Hedgehog (Post 14049984)
I know a lot of BBS Members don't advertise their birthday, but out of 6,944 members I would think at least 25% would. (Just look at this thread for example).

That would be a data base of 1,736 known birthdays. Divide that by the magic 23 and you get 75 sub-sets.

My fuzzy logic is that would mean at least 150 BBS members would have a birthday today (a minimum of 2 per 23 sub-set), yet the forums page shows there are only 5.

Stick that in your pipe and smoke it!

Simple and Stupid and I have the exact same birthday and age. Any other BBs ers share a like birthday.

Hedgehog 12-06-2021 12:53 AM

Quote:

Originally Posted by KYLIE MINEAGLE (Post 15837652)
Simple and Stupid and I have the exact same birthday and age. Any other BBs ers share a like birthday.

Nice bump of an old post from me... reading it, even I don't have a clue what I was talking about! :D

hughff 12-06-2021 01:01 AM

Quote:

Originally Posted by EdMan (Post 15836152)
I'm not sure that having 367 people in a room guarantees that at least two of them will have the same birthday. :angel:

Here's how it works.

1. The only requirement is that two people in the group share the same birthday. It doesn't have to be any particular day and they don't have to share it with you, just with someone else.

2. The first person in the group has a birthday, for example, 1st January. If the second person in the group is also born on 1st January then, boom, two people share a birthday and the set of two is sufficient. However, the odds of this are very low:1 chance in 365.25 or about 0.3%. (The extra .25 is for 29 Feb, which only happens every four years, of course.)

3. However, if the first person has a birthday on 1 Jan and the second has a different day (say 2 Jan) then close but no cigar. So bring in a third person. If that person has a birthday on either 1 or 2 Jan, then boom. Now the odds are actually 0.8% - I'll put the maths below.

4. If we keep repeating the process, by the time you get to 23 people it's 50% likely that two share a birthday. That's the paradox and, again, see below.

5. However, we want the odds to be 100%. So the first person in the group has a birthday on 1 Jan; the second person on 2 Jan, the third on 3 Jan... the 31st on 31 Jan, the 32nd on 1 Feb... the 60th on 29 Feb (that rare leap baby), the 61st on 1 Mar... and the 366th on 31 Dec. Whatever birthday the 367th has, they will share it with someone else in the group.

The maths:
  • For person 1, the chances are 100% because every date is clear. For person two, there's one day they would share with person 1, but the other 364 are clear, so their chance of a unique birthday is 364/365. For person 3 it's 363/365, and so on through to person 23, whose probability of having a unique birthday is 343/365.
  • To find the probability of everyone in the group having unique birthdays, we multiply all those 23 probabilities together, and if we do we end up with a probability of 0.491.
  • The probability that a birthday is shared is therefore 1 - 0.491, which comes to 0.509, or 50.9%.
But here's a website to do it for you. Note that after you have more than 85 people in a group (only 85!), the probability on the calculator reads 100% because the odds are now greater than 99.99%

EdMan 13-06-2021 08:45 AM

Quote:

Originally Posted by hughff (Post 15837659)
Here's how it works.

Actually I was talking bollocks. Having 367 people in a room does of course guarantee that at least two of them will have the same birthday. :supergrin:


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