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 Parade magazine's "Ask Marilyn" column, in which the world's highest IQ, Marilyn vos Savant, answered readers' questions and solved a wide variety of riddles and puzzles. riddles. The Monty Hall issue was sent in by a reader and posted exactly as follows: “Suppose you are on a game show and you have three doors to choose from: behind one door is a car; behind the others, goats. You choose a door, let's say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you: “Do you want to choose door number 2? » Is it in your interest to change your choice? » Craig F. Whitaker Columbia, Maryland Below is your Scholar's first published response to the above question. " Yes ; you should change. 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 choose door #1. Then the host, who knows there are doors behind them and will always avoid the one who wins the prize, opens them all except door #777,777. You'd pass through that door pretty quickly, wouldn't you? » 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 makes their first guess. Since there are two goats for a single car in the original scenario, there is a 2/3 chance that the player will initially choose a goat. So 2/3 of the time the host is forced to open a door because it's the only other door, besides the original door chosen by the...... middle of paper .... ..initial choice.Initial ChoiceHost OpenSecond ChoiceResultDoor 1Door 2Door 3Door Loss 1Door 2Door 4Door Loss 1Door 3Door 2Door Loss 1Door 3Door 4Door Loss 1Door 4Door 2Door Loss 1Door 4Door 3Door Loss 2Door 3Door 1Port e Window 2Door 3 doors 4 windows doors 2 doors 4 doors 1 windows doors 2 doors 4 doors 3 doors doors 3 doors 2 doors 1 windows doors 3 doors 2 doors 4 doors doors 3 doors 4 doors 1 windows doors 3 doors 4 doors 2 doors doors 4 doors 2 doors 1 windows doors 4 doors 2 doors 3LossDoor 4Door 3Door 1WinDoor 4Door 3Door 2LossBased on the possible outcomes (assuming the contestant still chooses to switch) shown above, if the contestant switches they have a 7/18, orInitial ChoiceHost OpensResultDoor 1Door 2WinDoor 1Door 3WinDoor 1Door 4WinDoor 2Door or 2 doors 4 doors lost 3 doors 2 doors lost 3 doors 4LossDoor 4Door 2LossDoor 4Door 3Loss