Companion code for my Number Guessing Game article - https://aparav.github.io/2018/01/08/the-number-guessing-game/

number-guessing-game.py

'''
Author: Aparajithan Venkateswaran
Companion Article: https://aparav.github.io/2018/01/08/the-number-guessing-game/
'''

from scipy.special import comb

def conditional_prob(i, k, n, m):
	'''
	Calculates the probability of event C conditioned on Ri
	'''
	if m == 0:
		return 0

	ans = i / m
	ans *= comb(m, i)
	ans *= comb(n - m, k - i)
	ans /= comb(n, k)
	return ans

def total_prob(n, m, k):
	'''
	Calculates the probability of event C
	'''
	probability = 0.0
	for i in range(0, k + 1):
		probability += conditional_prob(i, k, n, m)

	return probability

def checking_routine():
	'''
	Function to check arbitrary values of n, m, k and verify our hypothesis is true
	'''

	for n in range(1, 101):

		for k in range(1, n + 1):
			print("n = {} k = {}".format(n, k))
			expected_prob = k / n
			t_expected_prob = round(expected_prob, 7)

			for m in range(1, n + 1):
				probability = total_prob(n, m, k)
				t_probability = round(probability, 7)

				if t_probability != t_expected_prob:
					print("Expected: {}\nGot: {}\nn = {} m = {} k = {}".format(
						expected_prob, probability, n, m, k
					))
					return


if __name__ == "__main__":

	checking_routine()