How can the correctness of the Monty Hall problem solution be verified?

To verify the correctness of the Monty Hall problem solution, statistical modeling (simulation) is usually used. The idea is to run the experiment multiple times with different strategies (for example, always changing the door choice or always sticking with the initial choice) and compare the results.

Example in Python:

import random

def monty_hall_simulation(change_choice, trials=10000):
    wins = 0
    for _ in range(trials):
        prize = random.randint(0, 2)  # door with prize
        choice = random.randint(0, 2)  # player's choice

        # Host opens a door without a prize and not chosen by the player
        remaining_doors = [d for d in range(3) if d != choice and d != prize]
        opened = random.choice(remaining_doors)

        if change_choice:
            # Player switches choice to the remaining closed door
            choice = next(d for d in range(3) if d != choice and d != opened)

        if choice == prize:
            wins += 1
    return wins / trials

print("Probability of winning when switching choice:", monty_hall_simulation(True))
print("Probability of winning without switching choice:", monty_hall_simulation(False))

If the solution is correct, then the probability of winning when switching will be about 2/3, and when not switching — about 1/3. This approach allows you to verify and confirm the correctness of the problem's solution.