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Subject: "Lewis Carroll's Pillow Problem"     Previous Topic | Next Topic
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RAJITH RAVEENDRANATH (Guest)
guest
Jan-12-01, 01:20 PM (EST)
 
"Lewis Carroll's Pillow Problem"
 
   Reg. this problem : Lewis Carroll's Pillow Problem

This problem is cited by M. Gardner in his Mathematical Circus.
A bag contains a counter, known to be either white or black. A white counter is put in, the bag is shaken, and a counter is drawn out, which proves to be white. What is now the chance of drawing a white counter?

The explanation given as solution 2 is wrong as W2W1 and W1W2 are not 2 separate states as they are indistinguishable

I have a solution (#3 ) which gives the probability as 1/3 (SURPRISED !!)

The bag has equal probabilities of having W or B initially .
After a white counter put in and the two counters drawn one after the other, the following DISTINGUISHABLE combinations are there -

WW
WB
BW.

The first draw proved to be white . If the one inside is indeed white the combination we are looking for is WW. Probability (by definition) = No. of possible occurences/Total no. =
1(WW)/3(WW+BW+WB) = 1/3

Mail me your views !!



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alexb
Charter Member
672 posts
Jan-12-01, 01:28 PM (EST)
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1. "RE: Lewis Carroll's Pillow Problem"
In response to message #0
 
   RAJITH RAVEENDRANATH wrote:

> The explanation given as solution 2
> is wrong as W2W1 and W1W2 are not 2
> separate states as they are indistinguishable

It's a matter of terminology. You may say it's a single state to which one may arrive by two different routes. Then count the number of routes instead of states.

> I have a solution (#3 ) which gives
> the probability as 1/3 (SURPRISED !!)

Nah, nothing surprises me anymore.

> The bag has equal probabilities of
> having W or B initially. After a white
> counter put in and the two counters drawn
> one after the other, the following
> DISTINGUISHABLE combinations are there -

> WW
> WB
> BW.
>

> The first draw proved to be white.
> If the one inside is indeed white the
> combination we are looking for is WW.
> Probability (by definition) = No. of
> possible occurences/Total no. =
> 1(WW)/3(WW+BW+WB) = 1/3

This I do not understand. You have to discard either WB or BW - I do not know which one is "the first" for you - from your count. So, even according to your scenario, the answer should be 1/2 and not 1/3.

> Mail me your views !!

Please use one of the CTK Exchange forums to post your questions. Please do not use my email.

Thank you,
Alexander Bogomolny


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