Another day, another solution to a puzzle that I never got around to answering. Here is the puzzle again:
The Monty Hall problem is a famous puzzle based on an American TV game show. Please read the following problem and answer the poll based upon what you think you should do.
“You are a contestant on a game show. To decide your prize, you are asked to choose one of three doors (door 1, 2 or 3). Behind one of the doors is a car (good prize). Behind two of the doors is a goat (bad prize).
You choose door 3. The game show host, who knows what is behind each door, opens door 1 to reveal a goat. He then gives you the option to change your original selection to door 2.”
Is it better to stick with door 3, change your selection to door 2 or does it not matter?
The answer is below
It is better to change your selection to door 2. If you do this, the chance of winning the car is 2/3. If however you stick with door 3, the chance of winning the car is only 1/3.
Here is why. Initially, all doors have an equal chance of concealing the car (1/3). Therefore, the door that you pick has a 1/3 chance of concealing the car. Between them, the other two doors have a 2/3 chance of concealing the car (1 – 1/3). The host then opens one of these two doors to reveal a goat. The door with the goat then has a 0/3 chance of concealing a car. Thus, the other door that you did not pick has a 2/3 (2/3 – 0/3) chance of concealing the car.
Another way of looking at the problem is remember that due to the host never being able to open the door you chose, the chance of it concealing the car does not change from 1/3.