60% chance out of 25 people, someone shares your birthday

jensked · June 4th, 2005, 4:11 PM

Ok, my English isn't that good, but I'll try to explain. I hope I pick the right words.

When there are 26 (random) people in a bar, the chance that two of them share the same birthday, is 60%. That sound like bullshit, especially because there are 365 days and you are only with 26.

That's the beauty of the theory of probability.

What we are going to do, is to calculate the chance that nobody shares the same birthday. And then, we will distract (right term?) that chance from 100%.

Ok, here we go...

Step one
When there is only 1 person, the chance he does not share his birthday with anybody else is obviously 365/365.
When there is an extra 1 person, he can only have his birthday on the 364 other days. So the chance his birthday is on another day is 364/365.
When there enters a third person, the chance his birthday is on yet another day is 363/365.
...
You go on like that, and so the 26th person, has a 340/365 chance his birthday is not on the same day as the others.

Step two
Now we can calculate the chance that nobody shares the same birthday.
In the theory of probability, you have to multiply the seperate chances.
so: 365/365 x 364/365 x 363/365 x ... x 340/365 = 0.4 = 40%

Step three
So now we know that the chance nobody shares their birthday is 40%.
So the chance that two people out of 26 share their birthdays is 60%.

crazy, isn't it? images/smilies/smile.gif

jasonchiu · June 4th, 2005, 4:17 PM

ok we're in a virtual bar right here. my bday's is on may 9th WHOS IS THE SAME.?! (my guess is like 1)

Jostyrostelli · June 4th, 2005, 4:24 PM

I saw a program Brainiac yesterday hosted by Richard Hammond and he said the same.,.

jensked · June 4th, 2005, 4:28 PM

Seriously? images/smilies/smile.gif

Hehe, well, I didn't see it, I know this from my statistics-course.

Don't try this at home. You will be dissapointed.

ESPNSTI · June 4th, 2005, 4:40 PM

Your thread title is incorrect, it should read something like this:
"60% chance out of 26 people, 2 of them share a birthday" (not necessarily your birthday).

I think the changes of one of them sharing your birthday is something like this:
1. The chances of 1 other person sharing your birthday is 1 out of 365 (1/365).
2. The chance of a 2nd person sharing your birthday is also 1 out of 365, so combined for two people this is 2 out of 365 (2/365).
3. So the chances for 26 people (if you count yourself among them) is this:
(26-1) / 365 = 0.068 = 6.8%

Now it's been a lifetime ago since I took this kind of math in highschool (for which I got a near perfect score at the time), but still I could be wrong.

toma_alimosh · June 4th, 2005, 5:05 PM

aahhh, reminds me of high school data management, I really liked that course

zyran · June 4th, 2005, 5:06 PM

ESPNSTI you might be correct in some sense but you also have to consider the sample space. With the sample space you can truly identify the probability. Listing down the sample space would take ages though. 365P25.

pdanev · June 4th, 2005, 5:10 PM

oh god, how i hate probability threory and statics images/smilies/yucky.gif

jensked · June 4th, 2005, 5:35 PM

I'm very sure about my statement.

1) I was told about it by a professor in mathematics
2) It is featured in the book: Guys and Science
3) It was featured on Dutch television on the national science quiz
4) Someone told me Hammond explained it in Brainiac.

images/smilies/smile.gif

By the way, I had theory of probability 6 hours a week for a whole year long on the university. It is very un-logical. So that's why it sounds wrong.

ESPNSTI · June 4th, 2005, 5:46 PM

I wasn't saying your statement was incorrect, I was just saying that your title was.
The difference being:

The chances of 2 people sharing a birthday out of a pool of 26 people.

vs.

The chances of 1 or more people having the same birthday as yours out of a pool of 25 people.

chaos386 · June 4th, 2005, 5:56 PM

What if we want to check for a shared birthday across two different calendars (i.e. solar and lunar calendars)? Then what's the probability? images/smilies/mrgreen.gif

Viper007Bond · June 4th, 2005, 10:11 PM

Mmm, I think this is bullshit math.

Mischief007 · June 4th, 2005, 11:20 PM

In my high school class (long time ago images/smilies/wink.gif

), this girl and I shared the same birth date. Exactly the same.

Raheel · June 4th, 2005, 11:20 PM

don't remind me that i have a stats exam on wednesday... images/smilies/mad.gif

Leppy · June 5th, 2005, 8:07 AM

Quote:

Originally Posted by jasonchiu

ok we're in a virtual bar right here. my bday's is on may 9th WHOS IS THE SAME.?! (my guess is like 1)

I'll go along with this game only cause mine is on the 12th of may and thats dam close...

Wooptidoop · June 5th, 2005, 9:58 PM

04th June

Raheel · June 5th, 2005, 10:11 PM

mines 24th may....( turned 20 two weeks ago )

tloekke · June 6th, 2005, 12:36 AM

Josty and I share the same birthday.... Anyone else born on the 25th december?

bihus · June 6th, 2005, 12:42 AM

April 18th, here.

MixtriX · June 6th, 2005, 12:46 AM

^^ my mum is april 18.

mine is oct 18

June 4th, 2005, 4:11 PM	#1
jensked Joined: Mar 31st, 2005 Last Online: March 6th, 2010 Location: Flanders, Belgium Age: 26 Posts: 4,057 Car: 2006 Toyota Corolla Wagon Rep Power: 51	60% chance out of 25 people, someone shares your birthday Ok, my English isn't that good, but I'll try to explain. I hope I pick the right words. When there are 26 (random) people in a bar, the chance that two of them share the same birthday, is 60%. That sound like bullshit, especially because there are 365 days and you are only with 26. That's the beauty of the theory of probability. What we are going to do, is to calculate the chance that nobody shares the same birthday. And then, we will distract (right term?) that chance from 100%. Ok, here we go... Step one When there is only 1 person, the chance he does not share his birthday with anybody else is obviously 365/365. When there is an extra 1 person, he can only have his birthday on the 364 other days. So the chance his birthday is on another day is 364/365. When there enters a third person, the chance his birthday is on yet another day is 363/365. ... You go on like that, and so the 26th person, has a 340/365 chance his birthday is not on the same day as the others. Step two Now we can calculate the chance that nobody shares the same birthday. In the theory of probability, you have to multiply the seperate chances. so: 365/365 x 364/365 x 363/365 x ... x 340/365 = 0.4 = 40% Step three So now we know that the chance nobody shares their birthday is 40%. So the chance that two people out of 26 share their birthdays is 60%. crazy, isn't it? __________________

June 4th, 2005, 4:24 PM	#3
Jostyrostelli Joined: May 29th, 2004 Last Online: March 16th, 2010 Posts: 8,062 Rep Power: 33	I saw a program Brainiac yesterday hosted by Richard Hammond and he said the same.,. __________________ Your talents are not an achievement. What you do with them is. Owner of a 1970 Beetle 1300. (click for movies) Water is only to do the dishes.

June 4th, 2005, 4:28 PM	#4
jensked Joined: Mar 31st, 2005 Last Online: March 6th, 2010 Location: Flanders, Belgium Age: 26 Posts: 4,057 Car: 2006 Toyota Corolla Wagon Rep Power: 51	Seriously? Hehe, well, I didn't see it, I know this from my statistics-course. Don't try this at home. You will be dissapointed. __________________

June 4th, 2005, 5:06 PM	#7
zyran Joined: Mar 21st, 2004 Last Online: August 30th, 2007 Location: Malaysia Posts: 618 Rep Power: 0	ESPNSTI you might be correct in some sense but you also have to consider the sample space. With the sample space you can truly identify the probability. Listing down the sample space would take ages though. 365P25. __________________

June 4th, 2005, 5:35 PM	#9
jensked Joined: Mar 31st, 2005 Last Online: March 6th, 2010 Location: Flanders, Belgium Age: 26 Posts: 4,057 Car: 2006 Toyota Corolla Wagon Rep Power: 51	I'm very sure about my statement. 1) I was told about it by a professor in mathematics 2) It is featured in the book: Guys and Science 3) It was featured on Dutch television on the national science quiz 4) Someone told me Hammond explained it in Brainiac. By the way, I had theory of probability 6 hours a week for a whole year long on the university. It is very un-logical. So that's why it sounds wrong. __________________

June 4th, 2005, 4:17 PM	#2
jasonchiu Banned Joined: May 26th, 2004 Last Online: August 26th, 2005 Location: hong kong Posts: 5,216 Rep Power: 0	ok we're in a virtual bar right here. my bday's is on may 9th WHOS IS THE SAME.?! (my guess is like 1)

June 4th, 2005, 4:40 PM	#5
ESPNSTI Faded to black Joined: Dec 9th, 2003 Last Online: Yesterday Location: Decorah, IA Age: 38 Posts: 4,540 Car: 2004 Subaru Impreza WRX STI (USDM) LFS Status: Rep Power: 91	Your thread title is incorrect, it should read something like this: "60% chance out of 26 people, 2 of them share a birthday" (not necessarily your birthday). I think the changes of one of them sharing your birthday is something like this: 1. The chances of 1 other person sharing your birthday is 1 out of 365 (1/365). 2. The chance of a 2nd person sharing your birthday is also 1 out of 365, so combined for two people this is 2 out of 365 (2/365). 3. So the chances for 26 people (if you count yourself among them) is this: (26-1) / 365 = 0.068 = 6.8% Now it's been a lifetime ago since I took this kind of math in highschool (for which I got a near perfect score at the time), but still I could be wrong.

June 4th, 2005, 5:05 PM	#6
toma_alimosh Joined: Mar 14th, 2005 Last Online: 5:12 AM Location: The North American Foundry Age: 22 Posts: 3,424 Car: none as of yet Rep Power: 88	aahhh, reminds me of high school data management, I really liked that course

June 4th, 2005, 5:10 PM	#8
pdanev Joined: Oct 4th, 2004 Last Online: March 17th, 2010 Location: Netherlands Age: 26 Posts: 5,645 LFS Status: Rep Power: 30	oh god, how i hate probability threory and statics

June 4th, 2005, 5:46 PM	#10
ESPNSTI Faded to black Joined: Dec 9th, 2003 Last Online: Yesterday Location: Decorah, IA Age: 38 Posts: 4,540 Car: 2004 Subaru Impreza WRX STI (USDM) LFS Status: Rep Power: 91	I wasn't saying your statement was incorrect, I was just saying that your title was. The difference being: The chances of 2 people sharing a birthday out of a pool of 26 people. vs. The chances of 1 or more people having the same birthday as yours out of a pool of 25 people.

June 4th, 2005, 5:56 PM	#11
chaos386 .sa = bad driver! Joined: Nov 8th, 2004 Last Online: 8:11 PM Location: Al-Khobar, Saudi Arabia Age: 23 Posts: 4,795 Car: 2009 Seat Leon FR LFS Status: Rep Power: 191	What if we want to check for a shared birthday across two different calendars (i.e. solar and lunar calendars)? Then what's the probability? __________________ "Shit, that's a busy table cloth." -matt2000

June 4th, 2005, 10:11 PM	#12
Viper007Bond Lazy Head Dude Joined: Sep 21st, 2003 Last Online: 5:46 AM Location: Portland, Oregon Age: 25 Posts: 22,618 Car: Dodge Viper (I wish!) Rep Power: 340	Mmm, I think this is bullshit math. __________________ There is no replacement for displacement. - Wolfgang Bernhard, Chief Operating Officer, Chrysler Group talking about the Dodge Viper SRT-10 ... I ask Herb Helbig, vehicle synthesis manager for SRT and a member of the original Team Viper development group since day one, if they'd ever thought of adding traction control. "It comes with two," he says, pointing at my feet. "Learn to use them." Got it. - Motor Trend on the 2006 Dodge Viper Coupe, November 2005

June 4th, 2005, 11:20 PM	#13
Mischief007 Joined: Dec 3rd, 2004 Last Online: Yesterday Location: London, Ontario, Canada Age: 28 Posts: 4,538 Car: 2004 GP GTP CompG LFS Status: Rep Power: 31	In my high school class (long time ago ), this girl and I shared the same birth date. Exactly the same. __________________ 2004 Pontiac Grand Prix GTP CompG 71,464 km - 44,406 miles 14.4101 @ 94.67 mph

June 4th, 2005, 11:20 PM	#14
Raheel Photoshop Mod Joined: Mar 21st, 2005 Last Online: March 17th, 2010 Location: London UK, (Pakistani National) Age: 24 Posts: 1,565 Car: Local Busses and Trains Rep Power: 23	don't remind me that i have a stats exam on wednesday... __________________ 3aba7ech5hah: City University Racing

June 5th, 2005, 9:58 PM	#16
Wooptidoop Joined: Feb 7th, 2005 Last Online: 8:02 PM Location: Croatia Age: 25 Posts: 311 Rep Power: 24	04th June __________________ www.culig.hr

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June 5th, 2005, 10:11 PM	#17
Raheel Photoshop Mod Joined: Mar 21st, 2005 Last Online: March 17th, 2010 Location: London UK, (Pakistani National) Age: 24 Posts: 1,565 Car: Local Busses and Trains Rep Power: 23	mines 24th may....( turned 20 two weeks ago ) __________________ 3aba7ech5hah: City University Racing

June 6th, 2005, 12:36 AM	#18
tloekke Joined: Feb 4th, 2005 Last Online: October 18th, 2009 Location: Oslo, Norway Age: 28 Posts: 572 Car: Honda CR-V Rep Power: 21	Josty and I share the same birthday.... Anyone else born on the 25th december? __________________ Overheat is my hero!

June 6th, 2005, 12:42 AM	#19
bihus Joined: Dec 7th, 2003 Last Online: December 18th, 2008 Location: Portugal Posts: 4,618 Car: BMW 330Cd LFS Status: Rep Power: 30	April 18th, here.

June 6th, 2005, 12:46 AM	#20
MixtriX Joined: Jun 16th, 2004 Last Online: January 12th, 2008 Location: Melbourne, Australia (originally from London, UK) Age: 24 Posts: 533 Rep Power: 0	^^ my mum is april 18. mine is oct 18 __________________