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Hassony

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So you're in a game show, and the show host shows you 3 doors. Behind one door is a sports car worth $100,000, and behind the two other doors are two... goats.

 

You don't know what's behind each door, but the show host knows.

 

So you decide to pick door #1. You figure you have a 33.3% chance of getting the sports car.

 

However, after you chose door #1, the show host opens door #3 and reveals the goat behind that door.

 

So now, he asks you, "Would you like to change your answer and choose door #2 instead?"

 

If you're like most people, you will stick with your original choice since you figure that both door #1 and door #2 carry a 50% chance of you winning the sports car.

 

So what do you decide? Switch to door #2 or stick with door #1? In either case, why?

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The answer is meant to be that statistically you should swap. Always sounded like b****x to me, but I'm sure someone here can put me right.

 

EDIT: Ah, it's all to do with the fact that the host HAS to show you a goat after you make the first pick.

Edited by Gerry
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if you chose door one and he opened door three (to reveal a very sexy goat...)... ask him to open door one and pay attention. Door one means door one.

 

 

More seriously, you are in for 50/50 anyway. You could figure he chose not to open #1 as it does have the car, or you could figure he's bluffing and trying to make you stick with #1 knowing that the car is behind door #2. So 50/50 or better odds than that if you can spot a bluff...

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if you chose door one and he opened door three (to reveal a very sexy goat...)... ask him to open door one and pay attention. Door one means door one.

More seriously, you are in for 50/50 anyway. You could figure he chose not to open #1 as it does have the car, or you could figure he's bluffing and trying to make you stick with #1 knowing that the car is behind door #2. So 50/50 or better odds than that if you can spot a bluff...

 

That's not right...

 

I'm trying to remember the statistical explanation for it. But swapping increases you chances.

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Guest DanTheDaggerman

This is the bit that helps me remember this:

 

It may be easier to appreciate the solution by considering the same problem with 1,000,000 doors instead of just three (vos Savant 1990). In this case there are 999,999 doors with goats behind them and one door with a prize. The player picks a door. The game host then opens 999,998 of the other doors revealing 999,998 goats—imagine the host starting with the first door and going down a line of 1,000,000 doors, opening each one, skipping over only the player's door and one other door. The host then offers the player the chance to switch to the only other unopened door. On average, in 999,999 out of 1,000,000 times the other door will contain the prize, as 999,999 out of 1,000,000 times the player first picked a door with a goat. A rational player should switch.
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So you're in a game show, and the show host shows you 3 doors. Behind one door is a sports car worth $100,000, and behind the two other doors are two... goats.

 

You don't know what's behind each door, but the show host knows.

 

So you decide to pick door #1. You figure you have a 33.3% chance of getting the sports car.

 

However, after you chose door #1, the show host opens door #3 and reveals the goat behind that door.

 

So now, he asks you, "Would you like to change your answer and choose door #2 instead?"

 

If you're like most people, you will stick with your original choice since you figure that both door #1 and door #2 carry a 50% chance of you winning the sports car.

 

So what do you decide? Switch to door #2 or stick with door #1? In either case, why?

 

 

statistically it makes more sense to switch.

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The following reasoning seems to give the right answer, but is it correct? (I'm not sure it is):

 

There's a 2/3 chance that door 1 has a goat behind it

If door 1 has a goat behind it then door 2 MUST have a car behind it

If door 1 has a car behind it then door 2 MUST have a goat behind it

Therefore there's a 2/3 chance that door 2 has a car behind it

 

I reckon it depends on what the host does when he has a choice of doors to open: does he always open door 3 or is he equally likely to open door 2 or door 3?

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The following reasoning seems to give the right answer, but is it correct? (I'm not sure it is):

 

There's a 2/3 chance that door 1 has a goat behind it

If door 1 has a goat behind it then door 2 MUST have a car behind it

If door 1 has a car behind it then door 2 MUST have a goat behind it

Therefore there's a 2/3 chance that door 2 has a car behind it

 

I reckon it depends on what the host does when he has a choice of doors to open: does he always open door 3 or is he equally likely to open door 2 or door 3?

 

Depends whether the host was Jim Bowen or not!

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The following reasoning seems to give the right answer, but is it correct? (I'm not sure it is):

 

There's a 2/3 chance that door 1 has a goat behind it

If door 1 has a goat behind it then door 2 MUST have a car behind it

If door 1 has a car behind it then door 2 MUST have a goat behind it

Therefore there's a 2/3 chance that door 2 has a car behind it

 

I reckon it depends on what the host does when he has a choice of doors to open: does he always open door 3 or is he equally likely to open door 2 or door 3?

 

It's the fact that he HAS to open a door that makes the swithc worthwhile. If you've picked a goat and switch you will always win the car, therefore as you have a 2/3 chance of picking a goat you win 2/3 of the time by switching.

 

Here's another one, in Millionaire, you have 4 choices A, B, C, D. You chose one (let's say C) and then Chris removes two wrong answers leaving A and C. Should you stick, or twist or does it make no difference ?

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Here's another one, in Millionaire, you have 4 choices A, B, C, D. You chose one (let's say C) and then Chris removes two wrong answers leaving A and C. Should you stick, or twist or does it make no difference ?

depends what the question is

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It's the fact that he HAS to open a door that makes the swithc worthwhile. If you've picked a goat and switch you will always win the car, therefore as you have a 2/3 chance of picking a goat you win 2/3 of the time by switching.

 

Here's another one, in Millionaire, you have 4 choices A, B, C, D. You chose one (let's say C) and then Chris removes two wrong answers leaving A and C. Should you stick, or twist or does it make no difference ?

 

depends whether the 2 wrong answers are removed at random or not

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Here's another one, in Millionaire, you have 4 choices A, B, C, D. You chose one (let's say C) and then Chris removes two wrong answers leaving A and C. Should you stick, or twist or does it make no difference ?

 

No difference. The two random wrong answers can include your "choice". It's not the same as the goat problem, where the "wrong answer" has to be selected from one of the other doors. Now if you picked C, and then the computer had to reveal 2 wrong answers from A,B and D, then swapping would be the wise thing to do.

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No difference. The two random wrong answers can include your "choice". It's not the same as the goat problem, where the "wrong answer" has to be selected from one of the other doors. Now if you picked C, and then the computer had to reveal 2 wrong answers from A,B and D, then swapping would be the wise thing to do.

 

Tarrant wouldn't have the option to reveal the right answer either, though - just like the computer.

 

I reckon the question is fundamentally different, though, because it's more about knowledge and/or ability to make an intelligent guess with the answers whereas the goat/car thing is just a random choice.

 

If A's the right answer from A,B,C,D then it probably is from A and B as well.

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