Monty Hall Problem

Monty Hall’s problem is based on a game show, Let's make a deal, hosted by Monty Hall. In the show, the contestant has to choose a door out of three doors. Out of the three doors, there is one door containing a car and two containing goats. The contestant first chooses a door. The host, who knows what the door contains, will reveal another door with the goat. The contestant is then given a choice whether he wants to change or stay with the door he chose.

Since there are three doors to choose from, the initial choice is 1/3. After the contestant chooses one door, the chance of getting the car is still 1/3. After the host opens a door that contains a goat, the chances of getting the right door when you switch will become 2/3.

In all 3 Scenarios, the contestant chooses the first door.
Scenario 1: The first door has the car. The host reveals the door with a goat. If the contestant were to switch, he/she will get the goat instead of the car.

Scenario 2: The second door has the car. The host reveals the third door. If the contestant switches, he/she will get the car.

Scenario 3: The third door has the car. The host reveals the second door. If the contestant switches, he/she will get the car.

Hence, the chances are 2/3.

There are many misconceptions of the problem, for example, many people think that the choice is 1/3 and changed to 1/2 because there are only two doors left to choose from. However, as explained above, this is not the case.