This is a variation of the famous Monty Hall problem or Monty Hall paradox. The original problem was based on the game show Let's Make a Deal where you are given a choice of three doors where behind one door is a new car, and behind the other two, goats. No matter which door you choose, the host, knowing what is behind each door, always opens one of the remaining doors that has the goat, and asks if you want to switch. Is it to your advantage to switch?
The answer to this problem is counterintuitive and has generated many heated debates. You can find more information about this interesting problem by searching for “Monty Hall” on the internet. Here is an explanation of why switching is better:
Below are the three possible scenarios:
Door1 Door2 Door3
Goat Goat Car
Goat Car Goat
Car Goat Goat
If the contestant picks door 3, and the host opens a door with the goat (either door 1 or 2 in case 1, door 1 in case 2, and door 2 in case 3), then in two of the three cases shown above, he will win the car by switching. So the probability of winning by switching is 2/3. Thus it is advantageous to switch.
