The Birthday Paradox

[Louis]

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?

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[hughff]

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]

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]

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]

Originally Posted by ExiledStirling

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 To view the link you have to Register or Login But it tends to be more relevant to Americans that have watched Let's Make a Deal.

[ExiledStirling]

Originally Posted by Funk Butter

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]

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]

Originally Posted by ExiledStirling

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]

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]

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]

Hedgehog, you should never get a job in statistics.

[N Herts Eagle]

Originally Posted by Hedgehog

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]

Originally Posted by hughff

Hedgehog, you should never get a job in statistics.

Very true! :-)

[ceeby]

Originally Posted by hughff

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 )

[Worksop Palace]

Originally Posted by hughff

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]

Originally Posted by Worksop Palace

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]

Originally Posted by Away

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]

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

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Originally Posted by ExiledStirling

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]

Originally Posted by Finbar

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

To view the link you have to Register or Login

Good article to illustrate and explain it

[Funk Butter]

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.