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

jensked

jensked

Well-Known Member
Joined
Mar 31, 2005
Messages
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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? :)
 
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)
 
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.
 
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.
 
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.
 
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.
 
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? :mrgreen:
 
Mmm, I think this is bullshit math.
 
In my high school class (long time ago ;)), this girl and I shared the same birth date. Exactly the same.
 
jasonchiu said:
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)
Click to expand...

I'll go along with this game only cause mine is on the 12th of may and thats dam close...
 
Josty and I share the same birthday.... Anyone else born on the 25th december?
 
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