Calculate collision probabilities

collision.R

# Calculate the probability of a collision if `n` items are randomly drawn (with
# replacement) from a set with `total` number of items.
collision_prob <- function(n, total) {
  prob_no_collision <- 1
  # Do this in a loop instead of prod(numerators)/prod(denominators), because
  # that method is prone to result in a loss of precision due to rounding.
  for (i in seq(0, n-1)) {
    prob_no_collision <- prob_no_collision * (total - i) / total
  }
  1 - prob_no_collision
}

collision_prob(5, 9000)
#> [1] 0.001110679

collision_prob(5, 2^24)
#> [1] 5.960463e-07

collision_prob(12, 2^24)
#> [1] 3.9339e-06