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Post by Marshall on Mar 9, 2022 19:52:47 GMT
You are a contestant in a game show. There are three doors before you, behind one is a new car, behind the other two are goats and you have to pick one door.
You pick door #1. The host, who knows what's behind each door, opens door #3 to reveal a goat then asks, "Do you want to keep door #1 or switch to door #2?"
Will keeping door #1 or switching to door #2 offer the best odds of winning? (I'm assuming you want to win a car and not a goat.)
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Post by flatandy on Mar 9, 2022 19:56:49 GMT
The Monty Hall Problem.
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Post by Marshall on Mar 9, 2022 19:59:30 GMT
Yes. If you know the answer mum's the word.
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mids
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Post by mids on Mar 9, 2022 20:02:36 GMT
I'm sure I'm missing something but I can't see how it's anything other than makes no difference.
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Post by happyhammerhead on Mar 9, 2022 20:06:00 GMT
Our Computer Science teacher taught us this in 6th form.
Never heard of it called the Monty Hall Problem before though.
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mids
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Post by mids on Mar 9, 2022 20:08:52 GMT
Me neither, maybe he should stick to gardening?
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Post by wetkingcanute on Mar 9, 2022 20:10:28 GMT
This is a very old Quiz question.
In the first instance you are being offered a 1 chance in 3. You make your choice.
You are proved to have made the wrong choice.
You are then offered an 1 chance in 2 choice. - which are better odds (of course) than 1 in 3 - so mathematically the chances are you were wrong the first time so you should change your choice.
Which is all very hip and groovy - but you could have been right the first time.
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Post by Marshall on Mar 9, 2022 20:13:26 GMT
How are you proved to have made the wrong choice? It's still unknown what's behind door #1.
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Post by flatandy on Mar 9, 2022 20:14:31 GMT
Yes. WKC has it right.
Your door has a 33% chance of being a car. The other two have a 66% chance of being a car.
The host already knows the answer for one of the other two, and eliminates it, but the odds of the car being behind one of those two doors remains 66%.
Basically, the host's prior knowledge tips the game heavily.
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Post by Marshall on Mar 9, 2022 20:19:10 GMT
Wait, if one door is opened and there is a goat and the host "eliminates the other" by giving you the choice to switch then that would give you a 100% chance, no?
The host could be bluffing.
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Post by wetkingcanute on Mar 9, 2022 20:20:17 GMT
It would have been better for me to say "you are proved not to have selected the right door". Not "the wrong choice"
But still: First attempt you are offered 1 in 3.
Second attempt you are offered 1 in 2.
So the chances are that it was more difficult to guess correctly the first time and easier to second time - so change your choice.
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Post by Marshall on Mar 9, 2022 20:23:27 GMT
How? It could still be behind the original door you picked. You seem to be saying he will only give you the option to switch if you were wrong - but he could be bluffing you.
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Post by flatandy on Mar 9, 2022 20:34:16 GMT
You're not proven to be wrong. You always know that at least one of the other two doors will have a goat. All that happens is that your odds improve dramatically.
The host hasn't eliminated two goats. The host eliminates one goat, but eliminating that one goat means that all of your 2/3 odds are now resting on the second, unopened door that you didn't pick.
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voice
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Post by voice on Mar 9, 2022 20:35:47 GMT
We did this in school, the general gist is you are better to change your first choice
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Post by Marshall on Mar 9, 2022 20:44:39 GMT
Yes, it's better to switch, though it sounds pretty counter-intuitive (to me at least).
It's explained that all doors have a 33% chance to start. When one door is eliminated, your pick stays at 33% but the other door is now at 66%.
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Quiz Time
Mar 10, 2022 1:53:05 GMT
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Post by Repat Van on Mar 10, 2022 1:53:05 GMT
I would think technically the odds don’t change as you have made your choice?
So it makes no difference?
Or it could be that your odds went from 1 in 3 to 1 in 2. I don’t know.
But basically no, switching or staying won’t Improve your odds of winning.
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Quiz Time
Mar 10, 2022 1:54:45 GMT
via mobile
Post by Repat Van on Mar 10, 2022 1:54:45 GMT
This is a very old Quiz question. In the first instance you are being offered a 1 chance in 3. You make your choice. You are proved to have made the wrong choice. You are then offered an 1 chance in 2 choice. - which are better odds (of course) than 1 in 3 - so mathematically the chances are you were wrong the first time so you should change your choice. Which is all very hip and groovy - but you could have been right the first time. How are you proved to have made the wrong choice? You still don’t know where the car is. |
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Quiz Time
Mar 10, 2022 1:55:42 GMT
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Post by Repat Van on Mar 10, 2022 1:55:42 GMT
It would have been better for me to say "you are proved not to have selected the right door". Not "the wrong choice" But still: First attempt you are offered 1 in 3. Second attempt you are offered 1 in 2. So the chances are that it was more difficult to guess correctly the first time and easier to second time - so change your choice. How are you proved to have selected the wrong door? |
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voice
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Goals are a form of self inflicted slavery
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Post by voice on Mar 10, 2022 2:02:29 GMT
Its a statistic teaching thing if I remember correctly, where the car is is irrelevant to the exercise of the problem.
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Post by happyhammerhead on Mar 10, 2022 7:06:36 GMT
Yep, we were tasked with writing a program to simulate it. Swap or not and the results of both after thousands of iterations.
Quite a simple program iirc, and it proved swapping was favourable.
Funny thing is, when this was first posited, many prominent mathematicians utterly refused to believe it.
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