✔ 最佳答案
Your idea is right as the probability has not changed.
You must know one thing that, without knowing the answer in advance, there is no change in probability even one door was opened without the car ( and this door is not the one selected by you, of course ). If you have originally selected correctly then you still win the car without any change of idea.
Someone else may confuse by saying that, the original probability of getting the car is 1/3 but once the door was opened ( not your one ) without a car, the probability is risen to 1/2. Actually they have wrongly analyzed the problem. Let me explain for you.
No matter whether you have already selected the room with a car or not, among the two remaining room there must have at least one without car. The host simply opened it and try to affect your selection. However, it does not make sense for the car would not move between the rooms.
In the above case, the host just let you know a room without a car and actually the two events are now different with different pre-conditions. Hence, the arguments of those persons are incorrect because they confused two different events into one.
Hope I can help you.
參考: Mathematics Teacher Mr. Ip
