The Monty Hall Problem

The Monty Hall problem is a statistical brainteaser and is based on a challenge from an old game show called “let’s make a deal” and named after it’s host, Monty Hall. In the game, the contestant is given three doors to choose from. Behind one door hides the prized car, and behind the other two are goats. The contestant doesn’t not know what door contains what. Once the contestant has chosen a door, but yet to open it, the host will open one of the remaining doors. Now the host knows in advance what is behind each door, and will always open a door that contains a goat. The host then will give the contestant the option to change their choice to the remaining door or stay as is. Now the question is, is it better for the contestant to switch or stay with their initial choice?