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The Monty Hall problem is a puzzle in probability that is loosely based on the American game show Let's Make a Deal. The name comes from the show's host, Monty Hall. In this puzzle a player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host (who knows what's behind the doors) must open another door, revealing a goat. The host then must offer the player an option to switch to the other closed door. Does switching improve the player's chance of winning the car? With the assumptions explicitly stated above, the answer is yes — switching results in the chances of winning the car improving from 1/3 to 2/3.
The problem is also called the Monty Hall paradox, in the sense that the solution is counterintuitive, although the problem does not yield a logical contradiction.
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