Birthday Problem
How many people do we need in a class to make the probability that two people have the same birthday more than ½?
We have n classmates
365 days in a year (ignoring leap years)
Duplicates(n) = 1 – No duplicates(n)
We need to find the value of n where Duplicates(n) > ½
For us to have no duplicates, each person must not share the same birthday. The first person has 365 possibilities, the second has 364 possibilities, the third 363 possibilities, etc
Thus, we need to figure out the value where,
Below we try some values,
Therefore, the answer is n = 23
To simulate this in R, we can use the following code,
birthday_problem <- function(number_of_students) {
birthday <- 1:36
classmate_bdays <- sample(birthday,number_of_students, replace=TRUE)
duplicates <- classmate_bdays[duplicated(classmate_bdays)]
return (length(duplicates) != 0);
}
n<-23
rounds <-10000
results <- replicate (rounds, birthday_problem(n))
probability <- (length(which(results))/rounds)*100
probability
