That's the famous Monty Hall Dilemma. There are bunch of proves that claim switching the doors is to our advantage. Here is a simple version proposed in my class today. Instead of three doors we will consider 1001 doors with one car and rest of them are goats. Now the host opens 999 doors and you see all are goats.
Same proof applies when there are three doors.
Here is something to keep you busy for a while. Walk through time is an on-line game designed for kids like me. Those who are above nine may go somewhere else. The horns honk, people going crazy, crackers, lot of noise and emotions in the Bronx right outside our apartment. The Bronx Bombers have done it again.