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Nuance in Monty Hall Paradox

Marilyn vos Savant has made a mistake. She knew the game show Let’s Make a Deal too well, that she assumed the rules of the game show also applied to the question she was asked.

On the website of Marilyn vos Savant, the original question could be found here :

“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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, “Do you want to pick door #2?” Is it to your advantage to switch your choice of doors?”

Interestingly, the original question never indicate any established rules of Let’s Make a Deal, which is critical to this question. Examination of the original question reveals that the host is not mandatory to open another door, i.e., the host could just open the door that is choosen. In this case, which the hose is free to choose opening the door directly or opening another door for you then asking you to switch, his choice of opening another door is probably in order to lead you away from winning the car. (Unforturenately, the rule of winning what ever showed behind the door is not metioned in the question either.)

For this reason, the “Marilyn’s question” is different from “Monty Hall Paradox.”

So how to solve “Marilyn’s question”?