I have a "New Three-Subject Question" and I'm looking for experts to answer my questions.
There are three doors, one of which has 5 million behind it, which you can get after you choose it. Suppose you and Xiao Ming each choose a door, you choose A, Xiao Ming chooses C, then the system opens B, and the result shows that door B did not win. Now the question is - if you can swap, are you willing to swap your choices with Xiao Ming, and why❓ - One explanation is that it is not necessary, because the probability of winning the remaining two doors is 1/2. One explanation is that you should switch. Suppose you choose A at the beginning, the probability of winning is 1/3, and the probability of winning the other two doors BC combined is 2/3. The system opens B and it is an empty door, then the probability of C is 2/3, and you should switch. But what if you are Xiao Ming? From Xiao Ming's point of view, the probability of AB is also 2/3. Since B is an empty door, the probability of A is also 2/3, so you should switch. Should I switch or not? I am so worried.
