# Monty Hall Problem

## What is it?

The Monty Hall problem is a probability puzzle in which a contestant must choose one of three doors, behind one of which is a prize, and is then given the option to switch their choice after one of the remaining doors is revealed to be empty. The counter-intuitive solution is that switching the choice increases the contestant's chance of winning.

The Monty Hall Problem is a probability puzzle named after the host of the television game show "Let's Make a Deal," Monty Hall. The problem demonstrates a counterintuitive aspect of probability that can be difficult to grasp at first. Here's a simple example to explain the concept:

Imagine you're a contestant on a game show. The host, Monty Hall, presents you with three doors: Door A, Door B, and Door C. Behind one of the doors is a brand new car, and behind the other two doors are goats. Your goal is to choose the door with the car behind it.

Here's how the game plays out:

- You choose one of the doors, say Door A.
- Monty, who knows what's behind each door, opens one of the other two doors to reveal a goat (for example, Door B).
- Monty then gives you the option to either stick with your original choice (Door A) or switch to the remaining unopened door (Door C).

The Monty Hall Problem asks: Should you stick with your original choice, switch to the other door, or does it not matter?

Intuitively, it might seem like there's a 50-50 chance of winning the car, no matter if you stick or switch. However, the surprising result is that you actually double your chances of winning ...