Monty Hall presents you with 3 doors. Behind one of the doors is a new car. Behind the other 2 doors, there's nothing.

You make your choice of doors.....

Then Monty opens one of the doors that you didn't choose - and there's nothing behind it. He then offers you the opportunity to switch your choice to the other unopened door.

Do you switch or do you stick with your original choice?

Why? (the answer is actually quite simple....)

you should always switch your choice, becuase he has opened a door that you have not chosen and there was nothing behind the door you know that you may have chosen the door with the car and you may not have. if you change your answer you have a 2 out of three chance of getting the car but if you stick with your original choice you only have a 1 in 3 chance of getting it, I can't remember the exact details but i know that you have a better chance if you switch.

This is the classic Monty Hall problem, and it is to your advantage to always switch doors (the probability of success over the long run is greater than 0.50, and is actually 0.67).

The following cases describe all of the possible scenarios. In 2 of these 3 cases, it is to your advantage to switch, so the probability of success is 2/3.

Case 1:
Your initial choice is the prize. Monty shows you an empty door. If you switch, you lose.

Case 2:
Your initial choice is an empty door. Monty shows you an empty door (the only other empty door!). If you switch, you win.

Case 3:
Your initial choice is the other empty door. Monty shows you an empty door (the only other empty door!). If you switch, you win.