1 in 27 people share your birthday.

[Elaborate]

I've heard quite a few times that you only need to get 27 people together in order for one to have the same birthday as you. I've never had it explained why it's 1:27 instead of 1:365. Do any staticians here know? Or is it just a myth?

[rwald]

The way I read it, if you've got 23 people in a room the chances are greater than 50% that at least two of them share a birthday. I don't remember the math behind it, though...but I remember that it was supported by math.

Note that it isn't someone having the same birthday as you. It's just any two people sharing a birthday. That's why the numbers are lower than you would expect.

[Dylab]

There is a nice article on this and other "coincidences" at the website of CSIOP here: http://www.csicop.org/si/9809/coincidence.html

The answer is so easy I am surprised even Rwald didn't figure it out. :) Think of it as the chances of NOT finding a person with the same birthday. The chances of another person not having the same is 364/365. The chances of another person not having either two would be (364/365)(363/365). And so forth. By 23 (according to the article) you should get a precentage less then 50.

Rwald is right this isn't same as you but just a coincidence. If it was one having yours it would be 364 to the power of the number of people over 365 of the number of people. The chances, of course, of them not having your birthday.

Edit: The first example is finding two people with the same birthday not the same birthday as you.

[rwald]

I just re-ran the numbers, and confirmed what I said in my previous post. Now, I'll show the math to prove it.

To calculate the probability of you finding someone with the same birthday as you would be easy: Each additional person in the room has a 1/365 chance of matching birthdays, so the chance that anyone in the room having your birthday is (n - 1) / 365, where n is the number of people in the room including yourself. Clearly, if there are 183 people in the room with you, then the chance of someone sharing your birthday is greater than 50%. But where does 23 come in?

That's when you look for the probability of any two people in the room matching birthdays. You could try working the above formula for the first person in the room, and then adding the same thing for the second person in the room (remembering to not count the first person. Of course, you'd need to continue down for everyone in the room. It's rather messy.

Fortunately, there's a much better way to compute this problem. Simply calculate how probable it is that everyone in the room has a different birthday, and then invert that. The chance that the second person matches the first is 364/365. The third person will be 363/365. Then, the forth person changes the probability to 362/365. You get the idea. You muptiply it together for all the people in the room (since they're all got to have different birthdays), and that's the probability that a given number of people won't share a birthday. As it happens, when you have 23 people, the chance that they all have unique birthdays is 49.27%. Which is to say, the probability that at least two people share a birthday 50.73%.

Edit: Dylab, it wasn't that I couldn't figure it out, it was that I thought it would take a really long post to explain it. As it did.

[Dylab]

Edit: Dylab, it wasn't that I couldn't figure it out, it was that I thought it would take a really long post to explain it. As it did. [/B]

Rwald: Sure... ;) I was pretty sure you could figure it out I just took the chance for a good ribbing.

Hopefully no one will mind this small hijacking but what are some common arguments you guys know that are based purely on coincidences. The first thing that comes to mind is the Lincoln - Kennedy assanation relations mentioned in the article mentioned in my first post. Another one a person at school told me was some weird coincidences with the death of the rapper Tupac. I fergot most of what he said except that everything was so broad that after analyzing it, it would seem improbable that the connections wouldn't be there.

[SpaceLord]

Originally posted by Dylab


Rwald: Sure... ;) I was pretty sure you could figure it out I just took the chance for a good ribbing.

Hopefully no one will mind this small hijacking but what are some common arguments you guys know that are based purely on coincidences. The first thing that comes to mind is the Lincoln - Kennedy assanation relations mentioned in the article mentioned in my first post. Another one a person at school told me was some weird coincidences with the death of the rapper Tupac. I fergot most of what he said except that everything was so broad that after analyzing it, it would seem improbable that the connections wouldn't be there.

Among other things, Tupac talked about death in his music a lot. Death is a common theme in nearly all rap music. And his last album, Machavelli, has the letters for "Am Alive" contained inside itself. Pretty weak arguments, at least the ones I have heard.

Visually:

[BrianT]

Not if your birthday is February 29.

[BillyJoe]

Whodini, does your graph mean that, in a room of sixty people, there is a 100% chance (probability = 1) that there will be two people with the same birthday????

[BillyJoe]

Well, I guess that curve never quite meets the horizontal line.

[shemp]

Originally posted by BillyJoe
Well, I guess that curve never quite meets the horizontal line.

It meets the line at 367 (taking February 29 into account). With 366 distinctive days, you could have 366 people with different birthdays. But the 367th person would have to match one of them.

[Elaborate]

Ah, that makes much more sense now. I'd been hearing it "someone will have the same birthday as you" instead of "two people will share the same birthday. Thanks.

[patnray]

The one in 23 or 27 thing is not about someone having the same birthday as YOU. It is that in any group of 23 (or 27) people, it is almost certain that 2 of them will have the same birthday. The odds are much better for this than for matching your birthday because any day could match. I forget how it is derived, but as Irecall it is not complicated....

----
Whodini, does your graph mean that, in a room of sixty people, there is a 100% chance (probability = 1) that there will be two people with the same birthday????
----


Well, it gets very close to 1, so close, that there is no good way to choose scale that reflects that graphically.

[rwald]

Patnray, read our earlier replies. We discuss the exact method for calculating this number (BTW, it's 23, not 27).

[Brown]

There are plenty of web sites that discuss this subject. Here is one. (http://www.dartmouth.edu/~chance/teaching_aids/Profiles/coincidence/section3_3.html)The birthday problem, of course, asks how many randomly chosen people must be selected before there is a better than even chance of at least one pair of matching birthdays (answer: 23). After solving this I introduce the "birthmate" problem, which asks how many people you must randomly select to have a better than even chance of matching your own birthday (answer: 253).

[PygmyPlaidGiraffe]

More fun with probability!

In February, 1992 an Australian investment group (2500 investors) attempted to buy all possible combinations of six numbers from 1 to 44 (a total of 7,059,052 tickets) for a Virginia state lottery that had a $27 million jackpot. The Virginia State lottery was the largest prize in the country that particular weekend and an attractive lottery as the prize was worth more the price of all the tickets.

Each ticket cost $1 The cost to cover all bets was less than 1/3 of the amount needed to "buy" the lottery in a state like N.Y. (N.Y. has 54 numbers). In addition, there were 2nd, 3rd, 4th place prizes making the grand prize worth more.

The logistics of accomplishing the purchase were exraordinary.
The risk was the possibility of having to split the jackpot with other winners.
If the group won, an individual would have a 4 to 1 return on their speculative investment.

The group managed to buy about 5 million tickets before time ran out. The group had a 5/7 chance of winning.

Fortunately for the investors their gamble paid off, they won and had the only winning ticket.

The group's tactic highlighted many weeknesses in this lottery and other states applied the lessons learned. State lottery eligibility rules are constantly being reviewed and revised as individuals and groups challenge the rules and paradigm of lotteries.



"Pluralitas non est ponenda sine neccesitate" - William of Ockham

[LucyR]

Apropos nothing, but I imagine that it's an utter fabrication that you were born in the veldt.

What made you choose your user name?

[BillyJoe]

Originally posted by shemp
It meets the line at 367 (taking February 29 into account). With 366 distinctive days, you could have 366 people with different birthdays. But the 367th person would have to match one of them. Of course.

Yes, I was thinking about sixty people and how the curve seemed to meet the horizontal line at p = 1. However I quickly realized that, in fact, it did not do so. But, yes, you are right it does meet the horizontal at 367 people.

[Interesting Ian]

Originally posted by Elaborate
I've heard quite a few times that you only need to get 27 people together in order for one to have the same birthday as you. I've never had it explained why it's 1:27 instead of 1:365. Do any staticians here know? Or is it just a myth?

Then you've been misinformed. I've even seen this claim in the Sunday Times! (uk newspaper). It is more clear than anything could be that you would need about at least 200 people (possibly slightly less) in order for the probability to be greater than 50% that someone shares the same birthday as you. What amazes me is the stupid things people will believe, simply because they believe it has an authoritive source.

[Interesting Ian]

Originally posted by rwald
The way I read it, if you've got 23 people in a room the chances are greater than 50% that at least two of them share a birthday. I don't remember the math behind it, though...but I remember that it was supported by math.

Note that it isn't someone having the same birthday as you. It's just any two people sharing a birthday. That's why the numbers are lower than you would expect.

But people always use this birthday example to demonstrate what a poor grasp of probability people have, and yet it seems to me that a lot of them interpret the claim the same way as Elaborate does. So in terms of demonstrating peoples poor understanding of probability, it is debatable whether it does that. However in demonstating peoples capacity to obediently believe what authoritive sources say, and subcribe to the most patently false beliefs, it is unsurpassed.

[Interesting Ian]

Originally posted by Dylab
There is a nice article on this and other "coincidences" at the website of CSIOP here: http://www.csicop.org/si/9809/coincidence.html

The answer is so easy I am surprised even Rwald didn't figure it out. :) Think of it as the chances of NOT finding a person with the same birthday. The chances of another person not having the same is 364/365. The chances of another person not having either two would be (364/365)(363/365). And so forth. By 23 (according to the article) you should get a precentage less then 50.



Hell isn't there an easier way than that?! This is the way I would do it, but then I've had no education in statistics and probability whatsoever, and I would have thought there would have been a more elegant way. But looking at this thread it certainly doesn't seem I've missed out on anything.

[Interesting Ian]

Originally posted by rwald
[B]I just re-ran the numbers, and confirmed what I said in my previous post. Now, I'll show the math to prove it.

To calculate the probability of you finding someone with the same birthday as you would be easy: Each additional person in the room has a 1/365 chance of matching birthdays, so the chance that anyone in the room having your birthday is (n - 1) / 365, where n is the number of people in the room including yourself. Clearly, if there are 183 people in the room with you, then the chance of someone sharing your birthday is greater than 50%. But where does 23 come in?



Well that's interesting. Just shows that people can think something is very clear and obvious and yet be hopelessly wrong. I'll let you work out where you've gone wrong.

[BillHoyt]

Originally posted by Interesting Ian


But people always use this birthday example to demonstrate what a poor grasp of probability people have, and yet it seems to me that a lot of them interpret the claim the same way as Elaborate does. So in terms of demonstrating peoples poor understanding of probability, it is debatable whether it does that. However in demonstating peoples capacity to obediently believe what authoritive sources say, and subcribe to the most patently false beliefs, it is unsurpassed.
This statement is unsurpassed for illogic. That some people misunderstand the question is proof of nothing other than their lack of understanding. When people do understand the question they tend to dismiss the correct answer because they have a poor grasp of probability.

What any of that has to do with your twisted view of the role of authority in science and mathematics is anybody's guess.

Cheers,

[Interesting Ian]

Originally posted by BillHoyt
But people always use this birthday example to demonstrate what a poor grasp of probability people have, and yet it seems to me that a lot of them interpret the claim the same way as Elaborate does. So in terms of demonstrating peoples poor understanding of probability, it is debatable whether it does that. However in demonstating peoples capacity to obediently believe what authoritive sources say, and subcribe to the most patently false beliefs, it is unsurpassed.
--------------------------------------------------------------------------------


This statement is unsurpassed for illogic.



In what way is my statement at all illogical never mind unsurpassed for illogic??



That some people misunderstand the question is proof of nothing other than their lack of understanding.



Trivially true and certainly wholly irrelevant to the point I was making. What's wrong?? Did you not understand it??




When people do understand the question they tend to dismiss the correct answer because they have a poor grasp of probability.



And how do you know they are understanding the question?



What any of that has to do with your twisted view of the role of authority in science and mathematics is anybody's guess.


if you don't understand my point there is something seriously wrong with you.

[BillHoyt]

Originally posted by Interesting Ian


In what way is my statement at all illogical never mind unsurpassed for illogic??



Trivially true and certainly wholly irrelevant to the point I was making. What's wrong?? Did you not understand it??




And how do you know they are understanding the question?



if you don't understand my point there is something seriously wrong with you.

:rolleyes:

[Interesting Ian]

Originally posted by Interesting Ian
[Originally posted by rwald
[B]I just re-ran the numbers, and confirmed what I said in my previous post. Now, I'll show the math to prove it.

To calculate the probability of you finding someone with the same birthday as you would be easy: Each additional person in the room has a 1/365 chance of matching birthdays, so the chance that anyone in the room having your birthday is (n - 1) / 365, where n is the number of people in the room including yourself. Clearly, if there are 183 people in the room with you, then the chance of someone sharing your birthday is greater than 50%. But where does 23 come in?


--------------------------------------------------------------------------------



Well that's interesting. Just shows that people can think something is very clear and obvious and yet be hopelessly wrong. I'll let you work out where you've gone wrong.

Worked it out yet rwald?

[PygmyPlaidGiraffe]

Originally posted by LucyR
Apropos nothing, but I imagine that it's an utter fabrication that you were born in the veldt.

What made you choose your user name?


No not born on a Veldt.

I was not willing to give to much info regarding where I am, and I try not to put too much emphasis on where people are located as it may cause me to apply characteristics to people that they do not exhibit.

The name, quite a few illogical unconnected reasons mainly:

a) I appreciated a stuffed animal a friend's child had, it was a plaid giraffe just a little over a foot tall.
b) The Veldt, because I read a short story by Ray Bradbury that really made an impression on me about 5 years ago (I believe it was about a nursery). Plus, giraffes can conceivably habitate a veldt.
c) I enjoy surreal concepts, though they may not be practical.
d) I can be silly.
e) If a PygmyPlaidGiraffe did exist it would pose no direct threat to any person... I can't imagine anyone taking offense or fearing such an animal. Perhaps I have a limited imagaination though.

There appear to be a lot of fears about many things in our natural world and groups in our society. No one, not even I can define the habits or niche of a live PygmyPlaidGiraffe as one has never been observed. My hope is that people will not have any preconceived notions about me from this handle. Admittedly I never expected anyone to ask me how I chose my handle.

f) I am examining new concepts and arguments and have a lot of development to do. I am curious and there is a whole world of ideas, many that are new to me. I am on jourrny that at times feels surreal.

The PygmyPlaidGiraffe seemed at the time to be an appropriate handle to represent me on the journey.


I am not sure that will satisfy your question LucyR. Thanks for asking btw.

regards

PPG

quote:
------------------------------------------------------------------------
"Pluralitas non est ponenda sine neccesitate" - William of Ockham

[PygmyPlaidGiraffe]

BTW, is there a spell check option available for this board?

[rwald]

Ian, I saw some other people quote 253 as the "when there is a 50% chance of someone sharing my birthday" number, so I assumed that I was wrong. Let's see if I can work out why...

Well, I was just adding the probabilities, which is one of the easiest ways to get incorrect answers in statistics. So I should have realized my mistake immediately. But how did they find the right answer? The chance the first person has a birthday different from you is 364/365, and the chance that the second person has a different birthday than you is also 364/365, and so on, so I guess the formula is (364/365)ⁿ < 0.5 . I'll go run that on my calculator and see what I get...

(364/365)²⁵² = 0.5010
(364/365)²⁵³ = 0.4995

Yep, I guess that's what they did. Anyway, thanks for pointing out my mistake, Ian.

[LucyR]

Originally posted by PygmyPlaidGiraffe



No not born on a Veldt.

I was not willing to give to much info regarding where I am, and I try not to put too much emphasis on where people are located as it may cause me to apply characteristics to people that they do not exhibit.

The name, quite a few illogical unconnected reasons mainly:

a) I appreciated a stuffed animal a friend's child had, it was a plaid giraffe just a little over a foot tall.
b) The Veldt, because I read a short story by Ray Bradbury that really made an impression on me about 5 years ago (I believe it was about a nursery). Plus, giraffes can conceivably habitate a veldt.
c) I enjoy surreal concepts, though they may not be practical.
d) I can be silly.
e) If a PygmyPlaidGiraffe did exist it would pose no direct threat to any person... I can't imagine anyone taking offense or fearing such an animal. Perhaps I have a limited imagaination though.

There appear to be a lot of fears about many things in our natural world and groups in our society. No one, not even I can define the habits or niche of a live PygmyPlaidGiraffe as one has never been observed. My hope is that people will not have any preconceived notions about me from this handle. Admittedly I never expected anyone to ask me how I chose my handle.

f) I am examining new concepts and arguments and have a lot of development to do. I am curious and there is a whole world of ideas, many that are new to me. I am on jourrny that at times feels surreal.

The PygmyPlaidGiraffe seemed at the time to be an appropriate handle to represent me on the journey.


I am not sure that will satisfy your question LucyR. Thanks for asking btw.

regards

PPG

quote:
------------------------------------------------------------------------
"Pluralitas non est ponenda sine neccesitate" - William of Ockham

I enjoyed that, thanks. :)

Edited to add:

Where I come from we'd say 'the veldt', but that may just be a colloquialism. Your use of the indefinite article may be correct.

[Skeptoid]

Originally posted by PygmyPlaidGiraffe
BTW, is there a spell check option available for this board?
Hi, welcome to the forum. Sorry, no spell check option here but if your browser is Internet Explorer, you might try ieSpell v1.1. (http://www.iespell.com/) Freeware that works well.

[PygmyPlaidGiraffe]

Originally posted by Skeptoid

Hi, welcome to the forum.

Thankyou for the welcome and guidence Skeptoid.

PPG