# Birthday probability

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**1**Senior Member

Thread Starter

Join Date: Feb 2005

Location: Greenwich Ct

Posts: 850

**Birthday probability**

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

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**7**Senior Member

Join Date: Aug 2005

Location: Russellville, Arkansas

Posts: 557

**Re: Birthday probability**

Bailey Boat - 2/8/2006 1:27 PM

04-18-19??............ and for my coming birthday I'd like.................I'll get back to you......

04-18-19??............ and for my coming birthday I'd like.................I'll get back to you......

04-18-19 Holy chit. I knew you were old, but d@mn

Oops! you just forgot the last 2 #'s....sorry lol.

1/21

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**8**Senior Member

Join Date: Nov 2004

Location: Amelia Island, FL

Posts: 4,782

**RE: Birthday probability**

byram - 2/8/2006 2:20 PM

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

Anyway mine is 03/20

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**9**Senior Member

Join Date: Nov 2004

Location: Amelia Island, FL

Posts: 4,782

**RE: Birthday probability**

Reel Boobs - 2/8/2006 3:47 PM

Quote:
I am trying to figure your math. 23 people and the probability of 2 having the same birthday is 50%? Wouldn't it be if 182.5 peole were in a room, the probability of 2 sharing the same birthdate would be 50%, correct?

Anyway mine is 03/20

byram - 2/8/2006 2:20 PM

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

Anyway mine is 03/20

Opps, I was wrong! Byram you are correct! Heres how it is explained............

So, what is the probability that no two people will share a birthday?

Again, the first person can have any birthday. The second person's birthday has to be different. There are 364 different days to choose from, so the chance that two people have different birthdays is 364/365. That leaves 363 birthdays out of 365 open for the third person.

To find the probability that both the second person and the third person will have different birthdays, we have to multiply:

(365/365) * (364/365) * (363/365) = 132 132/133 225,

which is about 99.18%.

If we want to know the probability that four people will all have different birthdays, we multiply again:

(364/365) * (363/365) * (362/365) = 47 831 784/ 48 627 125,

or about 98.36%.

We can keep on going the same way as long as we want. A formula for the probability that n people have different birthdays is

((365-1)/365) * ((365-2)/365) * ((365-3)/365) * . . . * ((365-n+1)/365).

If you know permutation notation, you can write this formula as

(365_P_n)/(365^n).

That's the same as

365! / ((365-n)! * 365^n).

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

We've made some progress, but we still haven't answered the original question: how large must a class be to make the probability of finding two people with the same birthday at least 50%?

We know that the probability of finding at least two people with the same birthday is 1 minus the probability that everybody has a different birthday, and we know how to find the probability that everybody has a different birthday for any number of people. The easiest way to find the right class size is to use a calculator to try different numbers in the formula. It turns out that the smallest class where the chance of finding two people with the same birthday is more than 50% is... a class of 23 people. (The probability is about 50.73%.)

D@mn, I hate being wrong!

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**12**Senior Member

Join Date: Sep 2005

Location: RustNeverSleeps,MA

Posts: 4,974

**RE: Birthday probability**

Reel Boobs - 2/8/2006 1:47 PM

Quote:
I am trying to figure your math. 23 people and the probability of 2 having the same birthday is 50%? Wouldn't it be if 182.5 peole were in a room, the probability of 2 sharing the same birthdate would be 50%, correct?

Anyway mine is 03/20

byram - 2/8/2006 2:20 PM

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

If there are 23 people in a room the probability of 2 people sharing the same birthday is 50%. THT is a much larger group so lets put em up there.

03-09 for me

PS. Its pretty slow at work today. This might take us thru the winter.

Anyway mine is 03/20

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**13**Senior Member

Join Date: Jun 2003

Location: Norfolk

Posts: 4,030

**Re: Birthday probability**

neckbone - 2/8/2006 1:57 PM

3/30

On the probability part, 4 other of my friends have the same bday as I do. Needless to say, it was one fun 21st birthday party that many people do not remember.

3/30

On the probability part, 4 other of my friends have the same bday as I do. Needless to say, it was one fun 21st birthday party that many people do not remember.

Mine too is 03\30!

The thirtyth birthday was kinda interesting.

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**16**Senior Member

Join Date: Dec 2002

Location: Columbia, SC

Posts: 1,721

**Re: Birthday probability**

thubert57 - 2/8/2006 4:20 PM

Quote:
DING, DING, DING ... We have a winner!!

Mine too is 03\30!

The thirtyth birthday was kinda interesting.

neckbone - 2/8/2006 1:57 PM

3/30

On the probability part, 4 other of my friends have the same bday as I do. Needless to say, it was one fun 21st birthday party that many people do not remember.

3/30

On the probability part, 4 other of my friends have the same bday as I do. Needless to say, it was one fun 21st birthday party that many people do not remember.

Mine too is 03\30!

The thirtyth birthday was kinda interesting.

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**17**Senior Member

Join Date: Nov 2004

Location:

Posts: 1,911

**Re: Birthday probability**

02-07, yesterday and I celebrated with my doctor. He had fun by pulling my fingernail off. 9 months ago he put 3 screws in finger. Last month one of them worked its way out thru the nail, which caused the nail to become in-grown, which than became infected and swoll up to the size of a big toe on the end of my finger. I did get some great pain pills out the deal. He'd of never seen me if I knew he was going to do that.

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**20**Senior Member

Join Date: Jun 2003

Location: Norfolk

Posts: 4,030

**Re: Birthday probability**

neckbone - 2/8/2006 2:27 PM

Quote:
Guess I need to get started on that batch of brew, so we'll have something to celebrate with.

thubert57 - 2/8/2006 4:20 PM

Quote:
DING, DING, DING ... We have a winner!!

Mine too is 03\30!

The thirtyth birthday was kinda interesting.

neckbone - 2/8/2006 1:57 PM

3/30

On the probability part, 4 other of my friends have the same bday as I do. Needless to say, it was one fun 21st birthday party that many people do not remember.

3/30

On the probability part, 4 other of my friends have the same bday as I do. Needless to say, it was one fun 21st birthday party that many people do not remember.

Mine too is 03\30!

The thirtyth birthday was kinda interesting.

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