#' Birthday Problem
#' @references \url{https://en.wikipedia.org/wiki/Birthday_problem}
#' @export
Birthday_Problem <- function(size, days = 366) {
if (!suppressMessages(require("Brobdingnag"))) stop("The package `Brobdingnag` was not installed")
BP <- function(n, year) {
if (n >= year) {
BP <- 1
} else {
birthday <- Brobdingnag::prod(Brobdingnag::as.brob(year:1)) / (Brobdingnag::as.brob(year)^n * Brobdingnag::prod(as.brob((year - n):1)))
birthday <- as.numeric(abs(birthday))
BP <- 1 - birthday
}
return(BP)
}
sapply(size, FUN = function(x) BP(x, days))
}
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