I love this problem
Best evidence ever that humans can't do statistics. No one you tell will ever believe you. Even if you 'prove' it to them with maths they still say, 'Ah, well, that's just in theory. In real life it is just 50:50'.
(, Fri 4 Mar 2011, 7:09, Reply)
I've never understood this problem
In that the way people try to explain the problem and don't clearly explain whether things are independent or not in the scenario they create. As soon as you stress that in this situation they aren't independent because the gameshow host knows what's behind all doors, always will choose the goat and bases his decision on that it becomes a bit clearer...
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Herman Blume is unique, just like everyone else, Fri 4 Mar 2011, 8:28,
Reply)
It always made sense to me
if the guy always picks a goat then you've either already got the car (1/3 chance) or you picked a goat (2/3 chance) so it makes sense to swap.
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Peej, Fri 4 Mar 2011, 9:58,
Reply)
Yep
The first choice you make has a 1\3 probability of being right, however the second has 1\2 probability. The higher probability means that you should always go for it.
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LemonEntryMyDearWatson This time, Moriarty, the hand is on the other foot, Fri 4 Mar 2011, 10:51,
Reply)
All you need to make them realise how the maths works
is to explain to them that they can still pick the door with the goat shown if they like. When they obviously don't, ask them why not. Explain how their decision has changed it to a different game. Ask them if it would affect their choice of switching if, instead of opening another door with a goat, their door was opened and shown to have a goat.
(, Fri 4 Mar 2011, 11:26, Reply)
In part it could be the endowment effect in play
Great simulator. I liked doing it one at a time for some reason.
My take is that people don't like the idea of switching because they feel like they've made their choice and they 'own' what is behind that door. People are convinced that it's not worth switching, even if you point out that if they are right about the stats, then switching is no worse.
(, Fri 4 Mar 2011, 11:34, Reply)