Monty (Python) Hall Problem

Using programming and python to explain the Monty Hall Problem.

Pre-requsite Knowledge:

• Understanding of if/else statements, arrays and boolean expressions
• Know how randint() and random() from Python's Random library work
• Python programming language syntax
• General understanding of probability is a plus

The functions in this program are designed to return True if switching doors would result in the player winning the car.

Simulation Functions:

simulate: Written to be as true to the Monty Hall Problem as possible. Not programically optimized.

simulateSimplified: Takes the simulate function and iterates by simplifying the core logic. This simplification is designed to explain the Monty Hall Problem.

simulateSimplifiedFurther: Iterates further on simulateSimplified, reducing all logic down to a basic probability of success.

Helper Functions:

run: Used to run many iterations on our simulation functions and return the win rate.

Executation

We run simulate and simulateSimplified with the same sample size and same seeds.

• The results show the "simulated" probability of success if a player switches their door in the Monty Hall Problem.
• We use fixed seeds so simulate and simulateSimplified return the same results, proving they are functionally the same.