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

January 31, 2012
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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 problemrequire(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 = 200df = 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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