You are on a game show. The object of the game is to win a car. The host shows you three doors. Behind two of the doors there are goats. Behind the other door is a car. You select your door. The host says OK, but doesn't open your door. Instead, he opens one of the other doors to show you a goat (the host knows what's behind the doors and he opened a goat door on purpose). The host now says that you can still change your door if you want to. Or, you can stick with your original door.

What should you do, stay with your original door, or pick the other unopened door?

EDIT: Tell me the odds, don't just randomly say switch or stay.

Switch .

Quote from BloodFruit

Switch .

What are the odds you pick the car?

Stay .

Quote from muttonhead

What are the odds you pick the car?

50/50. this is a really stupid question.

Quote from notmaggot

50/50. this is a really stupid question.

Really, you think so? This is a logic riddle. I would not have posted it if it was that easy.

It is definetely NOT a 50-50 chance.

This problem is olde.

You switch, there's a higher chance of you winning, I forget how though.

There is one chance in three that the door you first picked is the correct one. This can't change just because you're shown there isn't a prize behind some other door. Since the prize has to be behind either the door you picked or the other closed door, and there is one chance in three that its the one you picked, there must be two chances in three its behind the other door. Switch, and you'll be right twice as often.

Quote from muttonhead

Really, you think so? This is a logic riddle. I would not have posted it if it was that easy.

It is definetely NOT a 50-50 chance.

that doesnt make any sense. jjiosdfdfjjifodjioejiewosedsfhuhuesuhsfufhusdhudhjusdfjusdjudsfhju /seizure

how would it not be? there are only 2 doors left. one has a goat the other has a car. its the same as flipping a coin.

It's 50/50 right?


edit: Oh wait no, it's one out of three.

Isn't it 0? If you choose the right door he's going to just open one of the other ones. If you pick a wrong one, he'll either open it anyways or just open the other wrong one.

This is really not that hard to understand, guys. You have a 2/3 chance of winning if you switch, every time.

There's a 1/3 chance of picking the car first, and the only time switching will cause you to pick a goat is if you choose the car.

There's a 2/3 chance of picking one of the goats first. Switching in this instance will get you the car.

Assuming you stay with your first picked choice, you only have a 1/3 chance of winning, because those are your odds of initially choosing the car. However, no matter what goat you pick (A or B), switching will always get you the car, because the other goat is eliminated from the odds. Switching from one goat can never get you the other goat. Staying is therefore illogical.

Think of it this way if this is confusing:

Options (Switching)

Pick the car first, switch, you lose

Pick goat A first, switch, you win

Pick goat B first, switch, you win

Options (Staying)

Pick the car first, stay, you win

Pick goat A first, switch, you lose

Pick goat B first, switch, you lose

You're given 2 options, each with 3 instances. One of the options allows you to win 2 out of 3 of those instances, while the other only allows you to win 1 out of 3 instance. Which would you rather go for?

It's not all that complicated.

As you can see in my graph, you have a 2/3 (75%) chance of getting the car if you switch.


http://img228.imageshack.us/my.php?image=ooooooooooommmmmmmmmmgglm2.png

With your original pick of the 3 doors, you have a 1/3 (25%) chance of picking the car. The odds say you picked wrong the first time, so you should switch.

EDIT: Exilement nailed it, good job.

Quote from muttonhead

1/3 (25%)

lol wut

Quote from muttonhead

2/3 (75%)

lol wut.