Verification of Monty Hall problem by experimental simulation.

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In the process of learning causal inference, I learned about the Monty Hall problem, and although I could see the process of the derivation, I still could not understand it very intuitively. Therefore, we hope to verify the Monty Hall problem through experimental simulations to verify the probability of final selection to the car caused by changing the selected door during the repetition of the experiment.

Through the experimental simulation, it was verified that changing the door of one's choice after the moderator opened a door could result in a higher probability of correct selection. Also, an explanation was found in the process of writing the code that the probability of choosing correctly at the beginning is 1/3, and if the choice is correct at the beginning, then not replacing the chosen door is the correct choice at that time; if the choice is wrong at the beginning, then replacing the chosen door at that time will get the correct choice, and the probability of choosing wrong at the beginning is 2/3.

Therefore, replacing the chosen door will get higher probability of success.