If you were on a game show?

Question

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.

Answer 1

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.

Answer 2

After the host has opened door number 3, it's a brand new game. You still have the option of choosing door number 1 or door number 2 by choosing to stay with door number 1 or change, so the odds are 50-50, so neither choice has an advantage.

I discount the idea that the host will open door number 2 next, just because he opened door number 3 first and door number 2 would be the next one on the list. If both dooors 2 and 3 are empty, there's nothing in the conditions that indicate that he didn't pick an empty door at random. If door number 1 is empty and door number 2 has the car, the host would of course have to open door number 3 if he's going to open any empty door, but you would have no way of knowing if he opened door 3 at random because he had to open any empty door, or if he opened door 3 because that's the only empty door left.

Another way of stating the problem is that there are two possibilities, the first being the host opened door 3 at random, meaning you should stay with door 1 because in this scenario door 2 must be empty; the other possibility being that the host picked door 3 because he had to, door 2 having the car, meaning you should switch to door 2. But since each possibility is equally likely, you're left with the same 50-50 chance.

The previous results have nothing to do with future probabilities, so the only thing you can say after finding out that door 3 is empty is that the car is behind either door 1 or 2, so either choice is as logical as the other.

Answer 3

I would switch to door 2, because theoretically speaking the host is opening the doors in squential order, given that he chose to open the last door first that means either he will go back and open door 2 and reveal it has nothing behind it which doesn't seem logical or he will then open door 1 and show nothing is behind it. This sounded better in my head.

Answer 4

There is no point in switching, you have a 50-50 chance of being correct. It's like a T-F question you don't know the answer to.

Answer 5

Do what I always do, pull out a gun, get the audience to turn out their wallets and then drive that new car to the chopshop for an easy 30 grand (depending on the car type of course).

Answer 6

Read the answer on the ask marilyn website, she says you should switch and tells why, I dont understand it, but you might...

Answer 7

steal the keys from the jerk!(he took my chance at a 2ND choice!!) the drive off accidentally hitting him on my way out!!