申論題

5. In Monty Hall problem, a contestant in a game show is shown three doors and told that behind one of the doors is a car, behind the other two doors are goats. The contestant Is asked to choose one of the doors and picks door no. 1. The game show host, who knows what is behind each door opens door no. 3, which reveals a goat. The game show then asks whether the contestant wants to switch with door no. I or switch to door no. 2. (30 pts).

(i) State the probability that the contestant picks door no. 1 for the first choice (e.g, 1/4, 2/5, etc,). (1 pt.)