Selecting a sheep or a car

There are three doors, two sheep and one car. After the guest chooses a door, the host opens one of the other two doors. The door contains sheep. Change or not. The grand prize will be given when there is a car behind the door. Otherwise, nothing exists.

 

I remember that I had to argue with little plums and madmen when I was doing this.

At that time, we still cannot determine that this is a probability problem.

In fact, this is not entirely a probability issue.

Because probability only considers the possibility of results. However, this problem is considered as a result.

In other words, it is in this event. It is a non-repetitive task. You can even consider the host's Psychology in making decisions.

Therefore, it is not a probability problem in the general sense.

Because the host's psychology has a very significant impact on this incident. If the host selects a random door and opens it, the host contains a goat. Then, you may have a 1/2 probability to change or not select you. If the host wants to open a sheep door, the probability of you selecting a car is 2/3. if this old man and the host are acquaintances, they can use this information to determine which car door is used.

There is a similar example: three prisoners, two of which are to be released. Prisoner A is familiar with the guard, but he cannot directly inquire whether he will be released. One of the other two will be released. Have you inquired about the release name of one of those two. Will it affect the probability of release?

Of course not. Everyone can understand this. But prisoner a actually changed the selected probability of the other two prisoners. In fact, I think it is impossible. The probability of a person not to be released is 0, and the other is 2/3. Will prisoner a be very happy to get the message "the other two are released? (A fool will be happy !)

If we have many awards to be awarded (in the form of a lucky draw ). Then you should be happy to hear others' names. Because you will win soon. However, if the two prisoners know that another person can be released at the same time. Is the probability that two prisoners will not be released is 2/3? Shouldn't it be 1/2? According to the conclusion given by the question of selecting a car and a sheep. This is indeed 2/3, so I never thought it was a probability problem. This is a game problem.

If the host is pretty tricky. None of his choices bring any information. So your choice is just starting from opening the door.

However, in any case, you change your past choices. In probability, it is beneficial to you. Because the probability of choosing another door is either equal or twice higher than that of sticking to one door.

Therefore, the optimal strategy is to change the selection.