A simulation for the TedEd frog riddle: https://www.youtube.com/watch?v=cpwSGsb-rTs

main.py

import random

N = 1000000  # number of frogs of each gender
assert N >= 2  # there must be at least 2 frogs of each gender

frogs = ["M"] * N + ["F"] * N

max_num_simulations = 2000000  # number of simulations to run
num_simulations = 0
num_clearing_successes = 0
num_log_successes = 0
while num_simulations < max_num_simulations:
    f = random.sample(frogs, 3)  # randomly select 3 frogs from population
    log_frog = f[0]  # the log frog is always the first frog
    clearing_frogs = [f[1], f[2]]  # the other two frogs are clearing frogs

    if "M" in clearing_frogs:  # if there is at least one male in the clearing
        if "F" == log_frog:  # if the log frog is a female
            num_log_successes += 1
        if "F" in clearing_frogs:  # if at least one of the clearing frogs is a female
            num_clearing_successes += 1
        num_simulations += 1

    if num_simulations != 0 and num_simulations % 100000 == 0:
        print(
            f"{num_simulations}, "
            f"{num_clearing_successes / num_simulations:.5f}, "
            f"{num_log_successes / num_simulations:.5f}"
        )


print("\n\n--- final results ---")
print("Prob Survival with 1 Frog:   ", num_log_successes / num_simulations)
print("Prob Survival with 2 Frogs:  ", num_clearing_successes / num_simulations)