You are taking part in a project. There are three doors, only one door has a car behind it, and the other two doors are empty. If you choose the car, you win. You choose one, and then the host will open an empty door in the remaining two, and then ask you if you want to change the other closed door.

You can understand it this way: there are two doors, one has a car and the other is empty. So the probability of choosing a car is 1/2. But there is a mathematician who understands it this way. If you choose to change forever, then you may win the car by choosing an empty door, because the owner will definitely open another empty door. So the situation has become your first choice to win the car with an empty net. The probability of choosing an empty door for the first time is 2/3, so the probability of changing cars and winning the lottery is 2/3, and the probability of not changing is 1/3.

This is the famous "three questions" and "three questions" (Monti? Hall? Question), also known as Monti Hall problem, Monti Hall problem or Monti Hall paradox, comes from the American TV game show "We? Manufacturing? Answer? Deal. An essentially identical problem was named "Three Prisoners Problem" in 1959. Prisoner? Question) in the form of martin gardner (Martin? Gardner's "Mathematical Games" column.

This question may have first appeared by Joseph Bertrand in 1889? Calcul？ Des? Probability? In a book. ? In this book, this problem is called "Bertrand's box paradox" (Bertrand's? Box? Paradox). The mathematician's answer can be changed, and the probability of change will be greater. If you don't change the door, the winning probability of the car is 1/3. If you change the door, the chance of winning the car is 2/3.