Birthday probability

[Dave]

Hi,

I can work out the probabilities for 2 people in the same room sharing a
birthday by dragging formula down like so

No People Different Same %
2 364 365 99.73% 0.274%
3 363 365 99.18% 0.820%
4 362 365 98.36% 1.636%


But can anyone get this equation into a single formula where I imput n for
the number of people in the room and the probability is calculated.

And secodly a formula for the probability as the same birthday as me

Dave

 

[Gary''s Student]

From Daytona Beach:

http://go.dbc.edu/mathematics/walsh_jennifer/files/CD6B9EA2F2254A399156D83E5943B498.pdf

 

[Bernard Liengme]

Your data seems wrong. It is generally accepted that about 23 people give a
50% chance of 'clash'
And after 100 it is essential 100%
Have a look at:
http://en.wikipedia.org/wiki/Birthday_paradox
Do not try to compute 365! (in Excel FACT(365))

 

[Dave]

Hi,

I'm confused, why do you say my data are incorrect? If I drag my formula
down then for 23 people I get a 50.73% chance that 2 people share the same
birthday and a 49.27% chance they don't

21 345 365 55.63% 44.369%
22 344 365 52.43% 47.570%
23 343 365 49.27% 50.730%
24 342 365 46.17% 53.834%
25 341 365 43.13% 56.870%

The formula in Column D dragged down is
D2 = =B2/C2
D3 = =B3/C3*D2 This is the dragged formula

Mike

 

[Dave]

Hi,

Thank you for that but it really is only a repeat of what I have done,what I
really wanted; and it might not be dooable, is a formula in a single cell
that works out the probability for n where n is the number of people in the
room.

D

 

[Gary''s Student]

O.K.

If A1 contains the number of people then:

=1-(PERMUT(365,A1)/365^A1)

 

[Dave]

Absolutely superb and thank you, I had been assured by a maths type person;
but never believed it, that there wasn't an Excel formula.

D

 

[Bernard Liengme]

Sorry that was not clear to me!

 

[Stan Brown]

Tue, 29 Jan 2008 04:52:00 -0800 from Dave

I can work out the probabilities for 2 people in the same room sharing a
birthday by dragging formula down like so

But can anyone get this equation into a single formula where I imput n for
the number of people in the room and the probability is calculated.

http://www.tc3.edu/instruct/sbrown/stat/birthday.htm

gives the formula and explains where it comes from. It makes the same
simplifying assumption that you do, ignoring leap years.