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Monty hall problem parade magazine
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The Monty Hall Problem: SL Portfolio
2005 Words5 Pages
Recommended: Monty hall problem parade magazine
Caitlin Elizabeth Connolly
2/24/14
IB Math SL
Casarico
IB Math SL Portfolio
The Monty Hall problem is a hallmark of modern statistics. It was first officially published in the “Ask Marilyn” column of Parade magazine, in which the world's highest IQ, Marilyn vos Savant, answered reader questions and solved an enormous variety of puzzles and riddles. The Monty Hall problem was sent in by a reader and published exactly as follows:
“Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows that's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?”
Craig F. Whitaker
Columbia, Maryland
Below is vos Savant's first published response to the above question.
“Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows that's behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You'd switch to that door pretty fast, wouldn't you?”
Marilyn vos Savant's answer assumes that the host is aware of the location of the car. In this case, the host will always open a door with a goat after the player makes their intiial guess. Because there are two goats to only one car in the original scenario, there is a 2/3 chance that the player initially chose a goat. Therefore, 2/3 of the time the host is forced to open a door because it is the only other door, besides the original door picked by t...
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...initial choice.
Initial Choice
Host Opens
Second Choice
Result
Door 1
Door 2
Door 3
Loss
Door 1
Door 2
Door 4
Loss
Door 1
Door 3
Door 2
Loss
Door 1
Door 3
Door 4
Loss
Door 1
Door 4
Door 2
Loss
Door 1
Door 4
Door 3
Loss
Door 2
Door 3
Door 1
Win
Door 2
Door 3
Door 4
Win
Door 2
Door 4
Door 1
Win
Door 2
Door 4
Door 3
Loss
Door 3
Door 2
Door 1
Win
Door 3
Door 2
Door 4
Loss
Door 3
Door 4
Door 1
Win
Door 3
Door 4
Door 2
Loss
Door 4
Door 2
Door 1
Win
Door 4
Door 2
Door 3
Loss
Door 4
Door 3
Door 1
Win
Door 4
Door 3
Door 2
Loss
Based on the possible outcomes (assuming the contestant always chooses to switch) featured above, if the contestant switches they have a 7/18, or
Initial Choice
Host Opens
Result
Door 1
Door 2
Win
Door 1
Door 3
Win
Door 1
Door 4
Win
Door 2
Door 3
Loss
Door 2
Door 4
Loss
Door 3
Door 2
Loss
Door 3
Door 4
Loss
Door 4
Door 2
Loss
Door 4
Door 3
Loss