#!/usr/bin/env python

# https://svn.red-bean.com/repos/kfogel/trunk/bin/n-rolls
# This code is in the public domain.  -Karl Fogel

# Suppose you have an N-sided die, and that you pick some random
# number R between 1 and N.  If you roll the die N times, what is the
# probability that *at least once* R will come up?
#
# Hat tip to Noel Taylor for the excellent problem.

import sys
import getopt
import random
import itertools

def main():
  if len(sys.argv) == 1:
    sys.stderr.write("Usage: %s N\n" % sys.argv[0])
    sys.exit(1)
  randy = random.SystemRandom()
  n = int(sys.argv[1])
  # Choose any number to be R.  Note that it should not (and
  # apparently does not) make a difference if you put the choosing of
  # R inside the outer 'iterations' loop below instead of here.
  r = randy.randrange(1, n + 1)
  # Arbitrarily do 10000 runs.
  iterations = 10000
  num_hits = 0
  for _i in itertools.repeat(None, iterations):
    for _j in itertools.repeat(None, n):  # roll the die N times
      if randy.randrange(1, n + 1) == r:
        num_hits += 1
        break  # We said "at least once", right?
  print "%.2f%% (%d / %d) of runs chose %d from the range 1-%d" \
    % (float(num_hits * 100) / float(iterations), num_hits, iterations, r, n)


if __name__ == '__main__':
  main()