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SORN
by OldSkrote - 31/07/25 02:07 PM
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Aug 24th, 2023
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Joined: Aug 2008
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Talk Morgan Expert
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It's 2. Switching doubles your chance of picking the car.
1972 4/4 2 Seater
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Moderate or good, occasionally poor Talk Morgan Addict
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Click here for the answer  As interesting as the answer is the number of people who refused to believe it when the problem was first published, including quite few with PhDs. In surveys only around 13% choose to switch. ~iw
2011 Morgan 4/4
1932 Austin 7 Chummy
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Needs to Get Out More!
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Needs to Get Out More!
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Thanks for posting that one. It gave me something to think about on the my drive back from Southwold to Paris today. On the one hand I thought that the probability argument that it makes sense to change (ie by changing you have a 2 in 3 chance of being right) is right in theory. However, intuitively, once one door has been opened you're into a 50/50 situation as far as the other two doors are concerned, in which case it makes no difference. Even having read your explanation above, I'm still not sure that I go along with the conclusion that it's better to change.
Giles. Mogless in Paris.
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Gone to Porsche Part of the Furniture
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OP
Gone to Porsche Part of the Furniture
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Click here for the answer As interesting as the answer is the number of people who refused to believe it when the problem was first published, including quite few with PhDs. In surveys only around 13% choose to switch. ~iw Uncle Ian, Does that mean i was right in a round about way 
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I first saw this problem on "The Royal Institution Christmas Lectures for Young People a few years ago (always worth a watch).
They way they demonstrated the solution was this. Imagine instead of three doors it's a pack of cards, face down. You pick one and if it happens to be the ace of spades you win. Out of the 51 remaining cards, the host turns over 50 of them to show that none of them are the ace of spades leaving one face down. Do you swap now?
~iw
2011 Morgan 4/4
1932 Austin 7 Chummy
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Gone to Porsche Part of the Furniture
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Gone to Porsche Part of the Furniture
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Doesn't the Channel 4 program Deal or no Deal have this principle, although i can;t stand NE i have watched snippets and it seems they can choose either the last box or the one they are holding.
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While we're on this sort of subject, I guess you are all familiar with the one about the 3 missionaries and 3 cannibals who all need to get across a river. They have a canoe which can take two people, but which cannot cross the river without someone to row it. The Missionaries cannot allow themselves to be outnumbered by the cannibals on either shore or they'll get eaten. How can they all get safely across ?
Perhaps as it's halloween I should have made that Vampires and Virgins rather than missionaries and cannibals; it would have been more PC too.
Giles. Mogless in Paris.
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Talk Morgan Expert
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Talk Morgan Expert
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Thanks for posting that one. It gave me something to think about on the my drive back from Southwold to Paris today. On the one hand I thought that the probability argument that it makes sense to change (ie by changing you have a 2 in 3 chance of being right) is right in theory. However, intuitively, once one door has been opened you're into a 50/50 situation as far as the other two doors are concerned, in which case it makes no difference. Even having read your explanation above, I'm still not sure that I go along with the conclusion that it's better to change. Look at it this way: initially you have a 2 in 3 chance of picking a goat; if you stay with that choice having been shown the wrong door you will still be 2 in 3 to pick a goat. If you swap doors then you transfer the 2 in 3 chance to the car.
1972 4/4 2 Seater
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Joined: Apr 2011
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Needs to Get Out More!
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Needs to Get Out More!
Joined: Apr 2011
Posts: 8,646 |
Thanks for posting that one. It gave me something to think about on the my drive back from Southwold to Paris today. On the one hand I thought that the probability argument that it makes sense to change (ie by changing you have a 2 in 3 chance of being right) is right in theory. However, intuitively, once one door has been opened you're into a 50/50 situation as far as the other two doors are concerned, in which case it makes no difference. Even having read your explanation above, I'm still not sure that I go along with the conclusion that it's better to change. Look at it this way: initially you have a 2 in 3 chance of picking a goat; if you stay with that choice having been shown the wrong door you will still be 2 in 3 to pick a goat. If you swap doors then you transfer the 2 in 3 chance to the car. I know, I get that. It's just that I still find it counter intuitive once you get to the two doors only knowing that behind one there is a goat and behind the other is a car. But then I always had these reservations about probability when I was doing my maths A level.
Giles. Mogless in Paris.
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Doesn't the Channel 4 program Deal or no Deal have this principle, although i can;t stand NE i have watched snippets and it seems they can choose either the last box or the one they are holding. This is the same as the Italian "Affari tuoi" that I mentioned previously.  likes to watch it. In last night's game the player was left with €50K and €100K still on the board. He chose not to swap and finished up with the €50K. It seems to me that swapping is usually the correct decision but I will take closer note in future. If I understand the Wikipedia article correctly the more initial choices there are the better chance there is that swapping is the correct decision.
Peter ![[Linked Image]](http://bradley.it/public_images/drive.jpg)
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