State Monty Hall problem and solve it.

The Monty Hall problem is a famous probability puzzle based on a game show scenario. The problem is named after Monty Hall, the original host of the American television game show Let's Make a Deal. The setup involves three doors: behind one door is a car, and behind the other two doors are goats. The contestant selects one door, and then the host, who knows what is behind each door, opens one of the other two doors to reveal a goat. The contestant is then given the opportunity to either stick with their original choice or switch to the other unopened door. The question is: what should the contestant do to maximize their chances of winning the car, and what is the probability of winning under each strategy?

Problem Setup

1. Three doors: There are three doors. Behind one of them is a car, and behind the other two are goats.
2. Initial choice: The contestant chooses one of the three doors.
3. Host’s action: After the contestant makes their choice, the host opens one of the remaining two doors, revealing a goat behind it. The host always knows where the car is, so they will never open the door that has the car behind __________ _________ _________ ____ _______ _______ ________ _____.
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