hypergeometric_distribution
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hypergeometric_distribution
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	#!/usr/bin/env python3

	import math
	import sys


	def binomial_coefficient(n, k):
	f = math.factorial
	return f(n) / f(k) / f(n - k)


	def compute(population_size, success_states_count, draws_count, observed_successes):
	N = population_size
	K = success_states_count
	n = draws_count
	k = observed_successes

	bc = binomial_coefficient

	return bc(K, k) * bc(N - K, n - k) / bc(N, n)


	def usage():
	print(f"Usage: {sys.argv[0]} <population size> <number of success states> <number of draws> <number of observed successes>", file=sys.stderr)


	def help():
	usage()
	print()
	print("Example:")
	print()
	print("In a Magic the Gathering deck of 60 crads, you've put 23 lands.")
	print("To compute the probability to get 3 lands in your opening hand (7 cards):")
	print(f" {sys.argv[0]} 60 23 7 3")


	def has_help_arg():
	help_args = ["-h", "--help", "/?", "/help"]
	return any([help_arg in sys.argv[1:] for help_arg in help_args])


	if __name__ == "__main__":
	if has_help_arg():
	help()
	sys.exit(0)

	if len(sys.argv) != 5:
	usage()
	sys.exit(1)

	try:
	numbers = [float(arg) for arg in sys.argv[1:]]
	probability = compute(*numbers)
	print(probability)
	except ValueError as e:
	print(e)
	usage()
	sys.exit(2)