Monty Hall Problem
The Monty Hall Problem
Introduction The Monty Hall Problem1 was created from the scenario introduced from the famous game show Lets make a deal2. The host (Monty Hall3) has three doors anxiously awaiting you and lets you know that behind two of the three doors are sad goats, and behind one of the three, is a brand new car. If you choose the car, you get to keep it. But, on the other hand if you unfortunately choose the goat, you are stuck with it. Monty finally asks you to make a decision between one of the three doors. After your careful decision, Monty opens one of the doors (one of the two that you didn’t choose) and reveals to you a sad goat. After the revealing of the sad goat, Monty asks you if you would like to switch your door. The question is, would switching your door either increase or decrease your odds of winning the car? The most common answer among all people and mathematicians alike would say that there is absolutely no difference at all if you switch, and if anything would say that it would decrease your odds. They would say that Monty showing us the goat would not give us new information. And that showing that one of the doors is a goat now only leaves us with a 50 50 chance to get the car. However, this assumption is clearly wrong, and the correct way to win is to actually make the switch, as it is going to nearly double your chances of winning, originally from 33% to 66%4. This is the theory that I will be testing in my project. The reason my project is important is because that learning more about this problem will be important to learning more about statistics. Also, learning about this theory could help me or someone else who is ever on a game show, by giving them a more statistical outlook on things and help them make better decisions. Also, can possibly help people win money on a game show!
Abstract
The Monty Hall Problem is a probability puzzle that states that switching the door you
Introduction The Monty Hall Problem1 was created from the scenario introduced from the famous game show Lets make a deal2. The host (Monty Hall3) has three doors anxiously awaiting you and lets you know that behind two of the three doors are sad goats, and behind one of the three, is a brand new car. If you choose the car, you get to keep it. But, on the other hand if you unfortunately choose the goat, you are stuck with it. Monty finally asks you to make a decision between one of the three doors. After your careful decision, Monty opens one of the doors (one of the two that you didn’t choose) and reveals to you a sad goat. After the revealing of the sad goat, Monty asks you if you would like to switch your door. The question is, would switching your door either increase or decrease your odds of winning the car? The most common answer among all people and mathematicians alike would say that there is absolutely no difference at all if you switch, and if anything would say that it would decrease your odds. They would say that Monty showing us the goat would not give us new information. And that showing that one of the doors is a goat now only leaves us with a 50 50 chance to get the car. However, this assumption is clearly wrong, and the correct way to win is to actually make the switch, as it is going to nearly double your chances of winning, originally from 33% to 66%4. This is the theory that I will be testing in my project. The reason my project is important is because that learning more about this problem will be important to learning more about statistics. Also, learning about this theory could help me or someone else who is ever on a game show, by giving them a more statistical outlook on things and help them make better decisions. Also, can possibly help people win money on a game show!
Abstract
The Monty Hall Problem is a probability puzzle that states that switching the door you