MONTY HALL PROBLEM

Monty Hall Problem is a classic probability puzzle that is based on a game show scenario. The problem is named after Monty Hall, who was the host of the game show "Let's Make a Deal" in the 1960s-70s. Here's how the problem works:

Suppose you are a contestant on a game show. The host, Monty Hall, presents you with three doors. Behind one of the doors is a valuable prize and behind the other two doors are goats.

You are asked to choose one of the doors, but you don't get to see what is behind it. After you make your choice, Monty Hall opens one of the other two doors to reveal a goat. He then asks you if you want to stick with your original choice or switch to the other unopened door.

The question is: Should you switch doors, or should you stick with your original choice? The surprising answer is that you should always switch! The probability of winning the prize if you switch is 2/3 and the probability of winning if you stick with your original choice is 1/3

The key to understanding the problem is to realize that Monty Hall's actions reveal information about the locations of the goats. By opening one of the doors and revealing a goat, he is effectively giving you new information that can help you make a better choice.