# THE MONTY HALL PROBLEM

### AN INTERESTING PROBABILITY PUZZLE

## Background

The Monty Hall problem is a probability puzzle loosely based on the American television game show Let's Make a Deal and named after the show's original host, Monty Hall. The problem, also called the Monty Hall paradox, is a veridical paradox because the result appears impossible but is demonstrably true.

## The Problem

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?

## Common mistake

Most people would suppose that both of the left doors have the same 1/2 chance of winning the car.

## Answer

The contestant should switch to the other door. Contestants who switch have a 2/3 chance of winning the car, while contestants who stick have only a 1/3 chance.

Null for the door opened, but 2/3 for the host's second still unopened door.

The Monty Hall Problem - Explained