Monty Hall Problem

This might sound extremely lame to some but it still amazes me how a probability can be doubled just after one single incident ie a change of variable.

Now imagine you're in a game show and there're three doors in front of you. Two of the doors have a goat behind each of them while behind the remaining door lies a car. Your job is to choose the door which will get you the car.

Say if this happens:
1. You choose Door 1.
2. Instead of being anti-climax and opens Door 1 straight away, the host opens Door 3.


3. You're lucky! Behind Door 3 is a goat!
4. Now the host gives you a choice to choose a door again.

Would you choose to stay with Door 1 or switch to Door 2?

For the solution, go here