Given a room with n people in it, what is the probability any two will have the same birthday?

January 31, 2012

Revisiting a fun puzzle I remember first encountering as an undergraduate. Nice example of creating a plot in R using ggplot2. I also plot the probability of someone in the room having the same birthday as you.

    
          ## See http://en.wikipedia.org/wiki/Birthday_problem for an explanation  of the problem
require(ggplot2)
require(reshape)
 
theme_update(panel.background=theme_blank(), 
			 panel.grid.major=theme_blank(), 
			 panel.border=theme_blank())
 
birthday <- function(n) { 
	1 - exp( - n^2 / (2 * 365) )
}
 
myBirthday <- function(n) {
	1 - ( (365 - 1) / 365 ) ^ n
}
 
d = 200
df = data.frame(n=1:d, AnyTwoSame=birthday(1:d), SameAsMine=myBirthday(1:d))
df = melt(df, id.vars='n')
 
ggplot(df, aes(x=n, y=value, colour=variable)) + geom_line() + scale_colour_hue('') +
	xlab('Number of People in Group') + ylab('Probability')

          view raw
          BirthdayProblem.R
          This Gist brought to you by GitHub.

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Jason Bryer

Given a room with n people in it, what is the probability any two will have the same birthday?

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