[GERMAN] "ziegenproblem"

[Gerhard Häring]

Peter Hansen wrote in comp.lang.python:
> Paul Rubin wrote:
>> 
>> stefan antoni <sasoft at gmx.de> writes:
>> > sorry that i won't be able to explain this in english, i don't know the
>> > name of this problem in english, and the website which is about this
>> > problem is also in german.
>> 
>> Usually we call it the "Monty Hall problem".  Monty Hall was the host
>> of a TV game show where he actually played that game (put a prize behind
>> one of three doors, etc).
> 
> See also http://c2.com/cgi/wiki?MontyHallProblem for full discussion.

Most of the explanations are too complicated IMHO. This is how I
finally understood the problem:

Your original choice has a chance of 1/3 to win the prize. This
doesn't change no matter what the moderator will do. Consequenetly,
the chance that the prize is hidden behind one of the two remaining
doors is 2/3.

So, now, the moderator opens one of the goat doors, but not yours.
Your original choice still has a chance of 1/3 to be correct, but the
two thirds for the other two doors now only apply to one door. That's
why switching doors is smart.

A little ASCII art :)

After your original choice:

 +------+  +------+ +------+
 |  ?   |  |  ?   | |  ?   |
 +------+  +------+ +------+
                   your choice

 \-------+--------/ chance to win:
         |             1/3
 chance to win: 2/3

         

 +------+  +------+ +------+
 | goat |  |  ?   | |  ?   |
 +------+  +------+ +------+
         chance to  chance to
         win: 2/3   win: 1/3

Gerhard
-- 
mail:   gerhard <at> bigfoot <dot> de       registered Linux user #64239
web:    http://www.cs.fhm.edu/~ifw00065/    OpenPGP public key id AD24C930
public key fingerprint: 3FCC 8700 3012 0A9E B0C9  3667 814B 9CAA AD24 C930
reduce(lambda x,y:x+y,map(lambda x:chr(ord(x)^42),tuple('zS^BED\nX_FOY\x0b')))