The Monty Hall Problem

You are a contestant in a game show. There are three doors, behind one of which is a prize. You are given the opportunity to select a door to open. Before you are allowed to open the door, the host opens another door to reveal that there is no prize behind it, and offers you the opportunity to change your mind. What should you do? This is also known as the Monty Hall problem.

Probability of winning after changing selection:

Probability of winning with original selection:

Sample size: