Prob of even distribution of n over k values.

probdist.py

import matplotlib.pyplot as plt
import random
import math

def get_prob(n, k, trials=200000):

    perfect = 0

    for _ in range(trials):

        nums = [random.randint(0, n - 1) for _ in range(k)]
        
        for i in range(n):

            if nums.count(i) != k // n:

                break

        else:

            perfect += 1

    return perfect / trials

###### Testing #######

n_tests = [1, 2, 3, 4, 5, 6, 8, 9, 10]
k_coefs = [1, 2, 3, 4, 5, 6]

plt.title("Noushin's Probability Theorem")
plt.xlabel('n')
plt.ylabel('Prob of even distribution')

legend = []

for coef in k_coefs:

    n_values = []
    prob_values = []

    for n in n_tests:

        p = get_prob(n, n * coef)
        
        print(n, ", ",  coef, "n - ", p)

        n_values.append(n)
        prob_values.append(p)

    plt.plot(n_values, prob_values)

    legend.append("k=" + str(coef) + "n")

plt.legend(legend)
plt.show()