A simple loop to calculate the combine hypergeometric distribution of repeated node selection to show a probability of selecting a malicious node

hypergeometric_distribution_loop.py

import math


def calculate_combined_probability_with_hypergeometric_distribution(total_population,
                                                                    sample_size,
                                                                    malicious_population,
                                                                    failure_threshold):
    failure_modes = {}
    sample_coefficient = math.comb(total_population, sample_size)
    for failure_sample in range(failure_threshold, sample_size + 1):
        # We'll iterate through the possible samples which represent a failure and calculate the probably of that
        # sample occuring in a hypergeometric distribution.

        # The number of ways to choose among the malicious population for a malicious cohort of failure_sample size.
        malicious_node_coefficient = math.comb(malicious_population, failure_sample)

        # The number of ways to choose the benign population among the sample size that's not among a failure cohort-sized sample
        selection_coefficient = math.comb(total_population - malicious_population, sample_size - failure_sample)

        failure_modes[failure_sample] = (malicious_node_coefficient * selection_coefficient) / sample_coefficient

    return failure_modes


failure_modes = calculate_combined_probability_with_hypergeometric_distribution(total_population=1000,
                                                                                sample_size=100,
                                                                                malicious_population=333,
                                                                                failure_threshold=51
                                                                                )

print(failure_modes)

combined_probability = sum(failure_modes.values())
print(combined_probability)

print("-----------------------------------------")