Well, the first term is almost over (I mean, lectures are over).. the exam is on Dec 11.. and I am already scared...
last post for this season... a brain teaser discussed by James Taylor (a prof at Ox, see below post for who he is)... seems like this is also a TV game in UK.... and most asked question in interviews!
There are three doors - one of them contains and if you call correctly you get it all. Other door contains nothing and you fail if you call it wrong...
Step 1: You can call a door as the door containing gold.
Step 2: The conductor gives a clue on the other two doors ("Door X does not contain gold") and he has to speak the truth.
Step 3: You can revise your call.
Big question: after knowing the clue, will you STICK to your door or SWITCH the doors?
lemme give an example...
Step 1: you call door 1
Step 2: Conductor says "Door 2 does not contain gold"
Step: will you STICK to your first door or SWITCH to the third door?
Answer is only one (not the "it depends" type)... and the reason can be given either in real life format or in theoritical (clue - probability)....
Any takers?
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2 comments:
I will STICK to my door.
The conductor being committed to speak only truth he is always going to point to door x that does not contain gold. That leaves always two doors that may contain the gold. The probability of one of the two doors containing gold is 50% no matter which one you choose.
So I would ignore the damn useless conductor's clue and STICK with my first choice.
Well, the answer is that, by thoery, you are expected to SWITCH to door 3.
Intuitive explanation:
Lets tweak the problem a bit. Lets say, we are working with 100 doors, instead of 3. And in step 2, the conductor can predict about the remaining 98 doors. (that is, 100 and 98 instead of 3 and 1).
Step 1: you call door 1
Step 2: Conductor now can predict something about 98 doors in doors 2 through 100. And he says “Door 2 does not have, door 3 does not have, door 4 does not have….door 46 does not have, door 48 does not have, … door 99 does not have, door 100 does not have”
You could see that when he had a chance to predict something about the rest of the doors, he chose to leave door 47 out. Now, in this situation, there are two options - either door 1 or door 47 has the gold and you need to choose one of these. Going by intuition, I would choose door 47, since the conductor decided to not predict about this.
So, Step 3: will you STICK to your first door or SWITCH to the 47th door? I will SWITCH to 47th door.
Now applying this to our problem, since the conductor decided to say crap on door 2, and stay silent on door 3 - we presume that Door 3 may have more probability to contain Gold and hence we SWITCH.
Again, this is just probability - by reality, Gold might still be in 1. You never know. It is just that Door 3 is a “highly probable” bet (which is the basis for pb to start with)…
Well, I hope I have not “lectured” too much in an effort to explain in detail. This answer can also be proved with Bayes probability theorem. Cheers!
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