Monty Hall Problem

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:

  1. You choose one of the doors, say Door A.
  2. Monty, who knows what's behind each door, opens one of the other two doors to reveal a goat (for example, Door B).
  3. 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 ...