Monty Hall problem Extension

The Monty Hall problem is a probability puzzle based on the American television game show "Let's Make a Deal". The name comes from the show's original host, Monty Hall. The problem is stated as follows: You are a contestant on a game show. The host of the show presents you with three doors. Behind one of the doors is a car, and behind the other two doors are goats. The host knows what is behind each door, and he asks you to choose a door. Assume you choose door number 1. Before the host opens the door you chose, he opens one of the other two doors, revealing a goat. In the example, the host opens door number 3. The host then asks you if you would like to switch your choice to the other remaining door. The question is, is it to your advantage to switch your choice? The answer is that you should switch doors. The probability of winning the car if you switch is 2/3, while the probability of winning the car if you stay with your original choice is 1/3. This is a counterintuitive result, as it seems that there are only two doors left, so the probability of winning should be 1/2. However, the key to understanding the problem is that the host knows what is behind each door and will always reveal a goat.