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

January 31, 2012 R

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')

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

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