Monty Hall Problem

I chose the Monty Hall problem because it is something that has perplexed me since I learned about it in high school statistics class. It stuck with me because it was one of those topics around which I could never quite grasp or accept. It is a little frustrating and I think about it every time I catch the revived version of Let’s Make A Deal on daytime television.


The Monty Hall problem revolves around a situation set in the game show, Let’s Make A Deal. The costumed contestant is faced with a choice; behind one of three doors, there is a car. If the contestant chooses the correct door, then he or she can keep the car. There are “zonks” or goats behind the other two doors which signify that the player has lost. Once the contestant chooses a door, the host, Monty Hall picks one of the other doors, always revealing a goat.


At this point it has been statistically proven that it is advantageous to switch to the other remaining door to increase the chance of winning the car. Intuitively, I at first assumed that each of the two remaining doors has a fifty percent chance of containing the car. However, this logic is incorrect, according to proven scholarly experiments and proofs.


It is said that the key to proving this problem lies with the host and his role in the situation. One must remember that he is aware of which door contains the car and which contain the goat. Therefore, he knows which of the two remaining doors have goats behind them. When the contestant chooses the first door, there is a one-third chance that it is the correct one. That means that there is a two-thirds chance that it is behind the remaining doors. When one of those doors is eliminated, there is still a two-thirds chance that it is behind the remaining door. The revealed door becomes a null option. Since two-thirds is greater than one-third, the contestant has a better chance if he or she changes her or her choice.


While this seems to make sense once explained, I still struggle understand and fully accept its authenticity because it does not seem logical. Actually, I kind of felt that way about a lot of topics in my statistics class.


1. Door

2. Goats

3. Car

4. Host (Monty Hall)

5. Contestant (in a funny costume)

6. Prizes

7. Zonk

8. Game Show (Let’s Make A Deal)

9. Television

10. Live Audience