Monty Hall Problem

The Monty Hall problem is a probability puzzle named after the host of the game show “Let’s Make a Deal,” Monty Hall. In the problem, you are asked to choose one of three doors. Behind one of the doors is a prize, while the other two doors hide nothing. After you have made your choice, Monty Hall reveals one of the doors that you did not choose, which is known to be a “losing” door with nothing behind it. Then, you are given the option to either stick with your original choice or switch to the other remaining door. The question is, should you stick with your original choice or switch to the other door?

Intuitively, it might seem that it doesn’t matter whether you stick with your original choice or switch, since the probability of winning should be the same either way. However, the correct answer is that you should switch doors.

To see why, consider the following: If you initially choose a door that does not have the prize behind it, then switching will give you a chance to win the prize. On the other hand, if you initially choose the door with the prize behind it, then switching will not change the fact that you have already won the prize. Therefore, switching doors will always increase your chances of winning the prize, no matter which door you initially choose.

This may seem counterintuitive at first, but it can be shown through a probability analysis. The probability of winning the prize by sticking with your original choice is 1/3, while the probability of winning the prize by switching doors is 2/3. Thus, switching doors is the better strategy.

― #genAI/chatgpt