birthday_problem.R

library(tidyverse)

# https://math.stackexchange.com/questions/35791/birthday-problem-expected-number-of-collisions
exp_collisions <- function(n, d) {
  n * (1 - (1 - (1 / d)) ^ (n - 1))
}

tibble(n = 1:80) %>% 
  mutate(collisions = exp_collisions(n, 365)) %>% 
  ggplot(aes(x = n, y = collisions)) +
  geom_point() +
  scale_y_continuous(breaks = function(x, n = 5) pretty(x, n)[pretty(x, n) %% 1 == 0],
                     minor_breaks = NULL) +
  scale_x_continuous(minor_breaks = function(x, n = 1) pretty(x, n)[pretty(x, n) %% 1 == 0]) +
  labs(title = "Expected number of shared birthdays",
       subtitle = "By size of organisation",
       y = NULL,
       x = "# of people")