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The Monty Hall Problem

Lasagna
Posts: 2,440
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7/28/2011 8:47:09 AM
Posted: 5 years ago
There are three doors; behind one is a brand-new car (that you win if you choose correctly) and behind the other two are goats. You pick door number one. Monty Hall shows you that there is a goat behind door number three. Does it significantly increase your odds to change your pick, knowing that there are only two doors left?

I maintained an adamant "no" for about fifteen minutes after hearing this, before I broke down and realized I was wrong. This is a slippery little problem!
Rob
Lasagna
Posts: 2,440
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7/28/2011 10:46:47 AM
Posted: 5 years ago
It doesn't matter, I just wanted to see if others would have as hard of a time as I did in figuring it out. I get the overwhelming feeling like there is still a 50% chance of getting it right if you don't switch - but that's obviously not the case if you understand the problem fully.
Rob
LeafRod
Posts: 1,548
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7/28/2011 10:57:58 AM
Posted: 5 years ago
At 7/28/2011 9:05:58 AM, Thaddeus wrote:
Switch, for obvious reasons.

It's dumber to say it's obvious than to admit you didn't get it at first
Thaddeus
Posts: 6,985
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7/28/2011 4:02:01 PM
Posted: 5 years ago
At 7/28/2011 10:57:58 AM, LeafRod wrote:
At 7/28/2011 9:05:58 AM, Thaddeus wrote:
Switch, for obvious reasons.

It's dumber to say it's obvious than to admit you didn't get it at first

Why? The solution is obvious.
freedomsquared
Posts: 450
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7/28/2011 4:07:44 PM
Posted: 5 years ago
The solution seems too obvious, so I might be wrong. However, I think I got it.
But it's Norway, sort of the Canada of Europe."
-innomen

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belle
Posts: 4,113
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7/28/2011 4:12:04 PM
Posted: 5 years ago
not gonna lie, it took several retellings for this one to click for me. its all in the way that you think about the problem.
evidently i only come to ddo to avoid doing homework...
freedomsquared
Posts: 450
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7/28/2011 4:14:55 PM
Posted: 5 years ago
Yea, I don't think I would've got it unless I was expecting a trick. Still, it took me a couple readings.
But it's Norway, sort of the Canada of Europe."
-innomen

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mongeese
Posts: 5,387
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7/28/2011 4:50:00 PM
Posted: 5 years ago
Car is in 1.
I pick 1.
2 or 3 is revealed.
I must stay.

Car is in 1.
I pick 2 or 3.
3 or 2 is revealed.
I must switched.

Therefore, there is a 2/3 chance that I should switch and a 1/3 chance that I should stay. Therefore, I should switch.
wjmelements
Posts: 8,206
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7/28/2011 4:53:25 PM
Posted: 5 years ago
At 7/28/2011 4:50:00 PM, mongeese wrote:
Car is in 1.
I pick 1.
2 or 3 is revealed.
I must stay.

Car is in 1.
I pick 2 or 3.
3 or 2 is revealed.
I must switched.

Therefore, there is a 2/3 chance that I should switch and a 1/3 chance that I should stay. Therefore, I should switch.

We've already seen this, so we should sit back and let them try to figure it out, but oh well.

It took me several minutes to figure it out, but I'm still proud I figured it out on my own.
in the blink of an eye you finally see the light
mongoose
Posts: 3,500
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7/28/2011 5:09:47 PM
Posted: 5 years ago
At 7/28/2011 4:53:25 PM, wjmelements wrote:
At 7/28/2011 4:50:00 PM, mongeese wrote:
Car is in 1.
I pick 1.
2 or 3 is revealed.
I must stay.

Car is in 1.
I pick 2 or 3.
3 or 2 is revealed.
I must switched.

Therefore, there is a 2/3 chance that I should switch and a 1/3 chance that I should stay. Therefore, I should switch.

We've already seen this, so we should sit back and let them try to figure it out, but oh well.

It took me several minutes to figure it out, but I'm still proud I figured it out on my own.

I didn't get it at first, but that's because I thought the person would try to reveal the car if they could, to make you lose, so you should stay. I didn't realize that only a goat could be revealed.
It is odd when one's capacity for compassion is measured not in what he is willing to do by his own time, effort, and property, but what he will force others to do with their own property instead.
Lasagna
Posts: 2,440
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7/28/2011 5:09:53 PM
Posted: 5 years ago
This really twisted me before I got it. I kept thinking... it's still 1/2 chance if I stick with my original choice after I learn the one that's not right, isn't it? How I eventually got it was realizing that they aren't actually just revealing ONE bad choice, they are revealing ALL the bad choices save one. You don't see this because all the revealed bad choices only = 1 . If there were 1,000 doors, and you picked door #1, and then all the bad choices save one were revealed (let's say doors 2-999) then it's easier to see.
Rob
Christopheratheist
Posts: 29
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8/14/2011 8:40:42 AM
Posted: 5 years ago
I looked at it in the sense that there is a 66.7% chance that the car is behind one of the other two doors that you didnt pick (before any are opened) once one of the others is opened to reveal a goat, effectively there is a 66.7% chance that it is in the other door you didnt pick