T1B8

The answer is YES! YOU SHOULD SWITCH!

The reason? Here it is.

You might think that with the probability of getting a goat, 2/3, by removing a goat the chance is now 1/2. So you get the same deal either way.

Well, after looking at the answers and doing a bit of math on my part, the problem is laid out like this:

Goat       Goat       Car

Say you pick door one

-> Goat       Goat       Car

Monty is forced to show you door 2--so he doesn't reveal the car and your door.

Therefore, assuming your door is a goat (which in this situation it is) you switch.

If:

Goat       Car       Goat

You still pick door one:

-> Goat       Car       Goat

Monty is forced to show you door 3--so you switch.

If:

Car       Goat       Goat

You pick door one:

-> Car       Goat       Goat

Monty can show you any door, and you shouldn't switch. If you do switch, however, you get a goat.

Assuming that he shows you door two, you assume you currently have a goat and switch. You miss the care. Assuming he shows you door three, you assume you currently have a goat and switch. You miss the car. There is a fifty-fifty chance of getting the car if you switch in both the door 2 and 3 instances.

HOWEVER:

You will find that if you switch, you have a higher probability of getting the car because two times out of three you will get the car. There is only one possibility in which you get the goat, and that is if your original door is the car.

Took me a while to wrap my head around the first time, then I came back to it later and it was a lot easier. The first time I read the answer the only word I took in was "2/3" and that didn't help at all. I drew a diagram to solve this question.

I really like this riddle.