The Monty Hall Problem (Observation, Simulations, and Proof Using Bayes Theorem)

We discuss the famous Monty Hall Problem, a probability puzzle inspired by classic game show "Let's Make.a Deal" hosted by Monty Hall. The problem can be succinctly stated as follows:

"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to switch your choice?"

It turns out to be to your advantage to switch, a result that confounds are intuition and expectations. We show how the information and probabilities lead to this answer, provide a Python simulation that demonstrates the result, and a proof using Bayes Theorem.

Original background music by Amanda Chaudhary.

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