lying.py

#!/usr/bin/env python3
import random

def truth():
    return random.randrange(3) == 2

# A, B and C toot the truth with a probability of 1/3 and lie with a probability of 2/3.
# A makes a toot and B toots an observation on whether or not A was tooting the truth or not. C toots that B confirmed A was truthful.
# What is the actual probability that A's toot was truthful?

def simulate(rounds=10000000):
    # All probabilities are probability of truthfulness
    count_total = count_true_when_c = count_false_when_c = 0

    for i in range(rounds):
        a_is_truthful = truth()
        b_is_truthful = truth()
        c_is_truthful = truth()

        # Did B confirm what A said?
        b_confirmed_a = (a_is_truthful and b_is_truthful) or (not a_is_truthful and not b_is_truthful)

        # Did C say B confirmed what A said?
        c_said_it = (b_confirmed_a and c_is_truthful) or (not b_confirmed_a and not c_is_truthful)

        count_total += 1
        if c_said_it:
            if a_is_truthful:
                count_true_when_c += 1
            else:
                count_false_when_c += 1


    return count_total, count_true_when_c, count_false_when_c


def main():
    print(simulate())


if __name__ == '__main__':
    main()