The Monty Hall Problem (Answer and Explanation) (7/13投稿記事の英訳）
Answer: The odds of the first door the participant selected having a car behind it are 1/3. The odds of the door Monty did not open having a car behind it are 2/3. Therefore, choosing to pick the other door is a wise choice.
Explanation 1: The odds of the participant`s first choice, door A, having a car behind it are 1/3. The odds of door A not having a car behind it are 2/3. In this case, the car is definitely behind either doors the participant did not select, B or C. Monty will open a door which does not have a car behind it, therefore, the car is definitely behind the door Monty didn`t open. The odds of this are 2/3. Accordingly, it becomes a wise choice for the participant to change their choice of doors.
Explanation 2: The odds of the participant`s first choice, door A, having a car behind it are 1/3. The odds of the car being behind door B, which the participant did not select at first, are 1/3. In this case, Monty opens door C. If you pick door B, you will win the car. The odds of the car being behind door C, which the participant did not select at first, are 1/3. In this case, Monty opens door B. If you pick door C, you will win the car. Therefore, after Monty opens a door with a goat behind it, changing your choice of doors gives you a 2/3 chance of winning, and is the best decision.
In the event that you don`t agree with the explanation given above, please see [1].
