Caitlin Elizabeth Connolly2/24/14IB Math SLCasaricoIB Math SL PortfolioThe Monty Hall problem is a hallmark of modern statistics. It was first officially published in the "Ask Marilyn" column of Parade magazine, in which Marilyn vos Savant, the world's highest IQ, answered readers' questions and solved a huge variety of puzzles and riddles. The Monty Hall Problem was submitted by a reader and posted exactly as follows: “Suppose you are on a television show and have a choice of three doors: Behind one door is a car; behind the others, goats. Choose a door, let's say no. 1, and the guest, who knows what is behind the door, opens another door, say no. 3, who has a goat. Then he says to you, "Do you want to choose door #2?" Is it to your advantage to change your choice?”Craig F. WhitakerColumbia, MarylandBelow is vos Savant's first published response to the above question.“Yes; you should change. The first gate has a 1/3 chance of winning, but the second gate has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million ports and you choose port #. 1. Then the guest, who knows what is behind the doors and will always avoid the one with the prize, opens them all except door no. 777,777. You'd get through that door pretty quickly, right?" Marilyn vos Savant's answer assumes that the host knows the location of the car. In this case, the host will always open a door with a goat after the player has his initial guess. Since in the original scenario there are two goats for one car, there is a 2/3 probability that the player initially chose a goat. Therefore, 2/3 of the time the host is forced to open one door because it is the only other door, besides the original door chosen by t......middle of the sheet......initial choice.Initial ChoiceHost opensSecond choiceResultDoor 1Door 2Door 3LossDoor 1Door 2Door 4LossDoor 1Door 3Door 2LossDoor 1Door 3Door 4LossDoor 1Door 4Door 2LossDoor 1Door 4Door 3LossDoor 2Door 3Door 1WinDoor 2Door 3Doors 4Doors 2Doors 4Doors 1Doors 2Doors 4Doors 3DoorsLoss 3Doors 2Doors 1Doors Windows 3Doors 2Doors 4Doors Loss 3Doors 4Doors Windows 3Doors 4Doors 2Doors Loss 4Doors 2Doors 1Doors Windows 4Doors 2Doors 3LossDoor 4Door 3Door 1WinDoor 4Door 3Door 2LossAccording to the possible results (assuming the contestant always chooses to switch) described above, if the contestant switches has a 7/18, or Initial Choice Host OpensResultDoor 1Door 2WinDoor 1Door 3WinDoor 1Door 4WinDoor 2Door 3Loss Door 2Door 4LossDoor 3Door 2LossDoor 3Door 4Door Loss 4Door 2Door Loss 4Door 3Loss