If you were on a game show?!

If you were on a game show?

and you were presented with 3 doors, two of which have nothing behind them, 1 has a new car. After choosing door number one, the host (who obviously knows where the car is) opens door number 3 to reveal that there is nothing behind it. You then get an option to switch to door number 2. What do you do and why? Best explained answer gets 10 points.

ALWAYS SWITCH!

When you first choose, you have a 1 out of 3 chance of being correct, Door A, B or C.

So you pick Door A. You have a 1/3 chance of being correct, and a 2/3 chance of being wrong.

The host (knowing which door has a car behind it) opens up another door (in this example, Door C) and asks if you want to switch or stay.

You should choose to switch because, as stated above, your probability of being WRONG with your first instinct is 2/3. This probability doesn't change just because you received more information because you received the information AFTER you have already made a decision.

So you switch, because the probability of being correct after the switch is 2/3, doubling your probability of winning a car.