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Monty Hall Problem

hgc

Penultimate Amazing
hgc
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Jun 14, 2002
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I know most of you are familiar with this one already, but we must settle it once and for all...

Monty presents 3 doors; behind one is a car, and behind the other two are goats. You pick a door. But before Monty opens that door, he reveals behind another door that there is a goat. He then gives you the opportunity to switch your choice. What is the probability that you will get the car by switching, or by staying?
 
hgc said:
I know most of you are familiar with this one already, but we must settle it once and for all...

Monty presents 3 doors; behind one is a car, and behind the other two are goats. You pick a door. But before Monty opens that door, he reveals behind another door that there is a goat. He then gives you the opportunity to switch your choice. What is the probability that you will get the car by switching, or by staying?
Click to expand...

What makes you think that we can settle this once and for all? Anyone dumb enough not to know the answer and stubborn enough not to read the literally thousands of web pages that dissect this to death is not going to be swayed, even by my deathless prose.
 
Re: Re: Monty Hall Problem

I agree with drkitten. How exactly is this not settled. Good God man, this has been proven to death. What is your point.
 
You will never settle it once and for all.

The answer depends on Monty's rules of behavior.

Want to create even more arguments? Here's another one that has the net bitterly divided:

You meet a woman with her son. She tells you she has two children. What is the probability the other child is a boy?
 
Well I say it's 50/50. Bite me, everybody!
 
rppa said:
Want to create even more arguments? Here's another one that has the net bitterly divided:

You meet a woman with her son. She tells you she has two children. What is the probability the other child is a boy?
Click to expand...

In this situation, 50%, because the child is specified by his presence.
 
Iconoclast said:
Oh God, it's happening again.
Click to expand...
Did we do this before? I've been hanging out here far too long.
 
rppa said:

You meet a woman with her son. She tells you she has two children. What is the probability the other child is a boy?
Click to expand...

Zero, because she's lying and has only one child.
 
new drkitten said:
Zero, because she's lying and has only one child.
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Yeah, that's what I said. She's running a social security scam by alternately dressing the kid in boy's and the girl's clothes so she can get extra benifits.
 
hgc said:
Did we do this before? I've been hanging out here far too long.
Click to expand...
I think we've done it about seven or eight times since the forums started, but it may have been mostly in the puzzles forum that it appeared. I'll stop derailing now, these threads are always a blast to watch.
 
Iconoclast said:
Yeah, that's what I said. She's running a social security scam by alternately dressing the kid in boy's and the girl's clothes so she can get extra benifits.
Click to expand...

Not to mention the huge variety of fake beards and noses.
 
hgc said:
I know most of you are familiar with this one already, but we must settle it once and for all...
.... What is the probability that you will get the car by switching, or by staying?
Click to expand...
I am more than happy to settle it for once and all.

There is a 100% probability that you will get the car by switching or by staying.
 
hgc said:

Monty presents 3 doors; behind one is a car, and behind the other two are goats. You pick a door. But before Monty opens that door, he reveals behind another door that there is a goat. He then gives you the opportunity to switch your choice. What is the probability that you will get the car by switching, or by staying?
Click to expand...

Here's my take on it.
 
Well, he'd always make sure you got the car if you hadn't had your guns taken away by limp-wristed liberals.
 
OK, sorry to keep this apparently unpopular thread going. I googled the problem, and one thing that was missing in my mind from all the "answer" pages was that, after the one wrong door is opened, why is the decision not now 1/2? You can either change, or you can keep your door. The prize can be behind either, so this new choice throws out the old choice of 1/3. This must obviously be the counterintuitive part of the answer, but my limited statistical knowledge makes me think it is more of a misunderstanding that there is now a new choice, not just a continuation of the original choice.
 
DaveW said:
OK, sorry to keep this apparently unpopular thread going. I googled the problem, and one thing that was missing in my mind from all the "answer" pages was that, after the one wrong door is opened, why is the decision not now 1/2? You can either change, or you can keep your door. The prize can be behind either, so this new choice throws out the old choice of 1/3. This must obviously be the counterintuitive part of the answer, but my limited statistical knowledge makes me think it is more of a misunderstanding that there is now a new choice, not just a continuation of the original choice.
Click to expand...
You are correct, sir.
 
DaveW said:
OK, sorry to keep this apparently unpopular thread going. I googled the problem, and one thing that was missing in my mind from all the "answer" pages was that, after the one wrong door is opened, why is the decision not now 1/2? You can either change, or you can keep your door. The prize can be behind either, so this new choice throws out the old choice of 1/3. This must obviously be the counterintuitive part of the answer, but my limited statistical knowledge makes me think it is more of a misunderstanding that there is now a new choice, not just a continuation of the original choice.
Click to expand...

imagine there are 100 doors instead of just 3. now imagine Monty asks you after each door is opened do you want to switch. when he gets down to 2 doors do you still think your original door has a 50% chance of being right?

right, it has a 1% chance. The same as when you originally chose.

this analogy helped me understand this puzzle when I first saw it.
 
HarryKeogh said:
imagine there are 100 doors instead of just 3. now imagine Monty asks you after each door is opened do you want to switch. when he gets down to 2 doors do you still think your original door has a 50% chance of being right?

right, it has a 1% chance. The same as when you originally chose.

this analogy helped me understand this puzzle when I first saw it.
Click to expand...
Or how about with the 100 door scenario, you pick a door, Monty reveals 98 goats. Do you still think you have a 99% chance by switching? That is the apt analogy.
 
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