The Monty Hall problem pg. 65 (Janice L, March 30th, 2008)
Christopher Boone, the protagonist of The Curious Incident of the Dog in the Night-Time by Mark Haddon, mentions the Monty Hall Problem in chapter 89. He has a fascination with math and science problems. In the book, he discusses and proves that the controversial answer Marilyn vos Savant offers to the Monty Hall Problem is in fact correct. Craig F. Whitaker sent the problem to vos Savant’s Ask Marilyn column in the Parade Magazine in 1990. Vos Savant supposedly has the highest IQ in the world. The problem is based on the American game show Let’s Make a Deal, hosted by Monty Hall.
Marilyn vos Savant Monty Hall
The Monty Hall Problem, which concerns probability, is this:
You are on a game show on television. On this game show, the idea is to win a car as a prize. The game show host shows you 3 doors. There is a car behind one of the doors and there are goats behind the other 2 doors. You pick the door you think contains the car. Then the game show host opens one of the doors you did not pick to show a goat. He/she offers you the opportunity to change your mind and pick the other unopened door. What would you do?
Marilyn vos Savant answered that you should change and choose the other door because there is a 2 in 3 chance that the car will be behind the final door. Many people, including math professors, wrote to Marilyn vos Savant and told her that her answer was incorrect. They followed their intuition and believed that there is a 50-50 chance of choosing the door with the car after the first door with the goat is opened. However, Christopher provides a proof of the problem and confirms that Marilyn von Savant’s response was correct.
There are 3 possible outcomes if a player is to switch doors:
1. The player originally chooses the door with the car. If he/she switches, he/she switches to a door with a goat.
2. The player originally chooses the door with Goat A. If he/she switches, he/she switches to a door with the car because the door with Goat B is already opened.
3. The player originally chooses the door with Goat B. If he/she switches, he/she switches to a door with the car because the door with Goat A is already opened.
Out of these 3 possible situations, 2 allow the player to win the car.
If the player did not switch doors, these would be the 3 possible outcomes:
1. The player originally chooses the door with the car. He/she wins the car.
2. The player originally chooses the door with Goat A. He/she loses the game.
3. The player originally chooses the door with Goat B. He/she loses the game.
Out of these 3 possible situations, only 1 allows the players to win the car.
Clearly, Marilyn vos Savant was correct in saying that the player should always change his/her mind when given the opportunity.
This diagram illustrates the different outcomes of the game:
Christopher uses the example of the Monty Hall Problem to demonstrate his love for math, numbers, and logic. Based on the responses to the problem, he states that many people uses their intuition to make decisions, but it can sometimes lead people to make the wrong ones. Therefore, logic is much more reliable, and it can help people to work out the correct answer.
For further information and more in-depth explanations, go to: pages 62 to 65, The Monty Hall Problem Web Page or Wikipedia.
Marilyn vos Savant Monty Hall
The Monty Hall Problem, which concerns probability, is this:
You are on a game show on television. On this game show, the idea is to win a car as a prize. The game show host shows you 3 doors. There is a car behind one of the doors and there are goats behind the other 2 doors. You pick the door you think contains the car. Then the game show host opens one of the doors you did not pick to show a goat. He/she offers you the opportunity to change your mind and pick the other unopened door. What would you do?
Marilyn vos Savant answered that you should change and choose the other door because there is a 2 in 3 chance that the car will be behind the final door. Many people, including math professors, wrote to Marilyn vos Savant and told her that her answer was incorrect. They followed their intuition and believed that there is a 50-50 chance of choosing the door with the car after the first door with the goat is opened. However, Christopher provides a proof of the problem and confirms that Marilyn von Savant’s response was correct.
There are 3 possible outcomes if a player is to switch doors:
1. The player originally chooses the door with the car. If he/she switches, he/she switches to a door with a goat.
2. The player originally chooses the door with Goat A. If he/she switches, he/she switches to a door with the car because the door with Goat B is already opened.
3. The player originally chooses the door with Goat B. If he/she switches, he/she switches to a door with the car because the door with Goat A is already opened.
Out of these 3 possible situations, 2 allow the player to win the car.
If the player did not switch doors, these would be the 3 possible outcomes:
1. The player originally chooses the door with the car. He/she wins the car.
2. The player originally chooses the door with Goat A. He/she loses the game.
3. The player originally chooses the door with Goat B. He/she loses the game.
Out of these 3 possible situations, only 1 allows the players to win the car.
Clearly, Marilyn vos Savant was correct in saying that the player should always change his/her mind when given the opportunity.
This diagram illustrates the different outcomes of the game:
Christopher uses the example of the Monty Hall Problem to demonstrate his love for math, numbers, and logic. Based on the responses to the problem, he states that many people uses their intuition to make decisions, but it can sometimes lead people to make the wrong ones. Therefore, logic is much more reliable, and it can help people to work out the correct answer.
For further information and more in-depth explanations, go to: pages 62 to 65, The Monty Hall Problem Web Page or Wikipedia.
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