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94#
 
 
發表於 2007-3-16 01:17 AM
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Originally posted by playbr2 at 2007-3-15 04:25 PM: 
引文一篇[/colo...   The comment is wrong, without another knowingly choose it for u, the probablity will be the same. 
 
first, Player 3 choose 1 ( win, lose, lose),  
*before opening the door, the porbably of each door is 1/3 for winning 
 
then, host 2 choose 1 (lose, lose) with the probabilty of 1/3 to pick this set or ( win,  lose) with the probability of 2/3 ,<-- this interferance is critical because the host have to choose the lose door in either situation.  
 
The host' probability of holding a winning door would be 1/2. Because in the cases of (lose, lose) with the probability of 1/3, he has to open the lose door, which left ( lose) door. And in the ( win,  lose) case with the probability of 2/3, the host has to open the lose door, which left ( win). 
As a result, with knowingly open ( lose) door, there are only 2 outcomes: 
( win)or ( lose). However, because the chance of picking a (lose, lose) is only 1/3, there are 2/3 of chance that the host will have ( win) 
 So the probability is 2/3 
-------------------------------------------------- 
In case the host DOES NOT knowingly open the ( lose) door 
first, Player 3 choose 1 ( win, lose, lose),  
*before opening the door, the porbably of each door is 1/3 for winning 
 
then, host 2 choose 1 (lose, lose) or ( win, lose), 
 
Without knowingly open the ( lose) door the host's probability of holding a winning door would be 1/2. Because in case of (lose, lose) with the porbability of having this set is 1/3 and in case of (win, lose) the porbability is 2/3.  
So,withouth knowingly pick the set, the chance shall be [1/2x1/3 +1/2x2/3]=1/2 
 am not expert in stats and i dont think my ans is right anyways  
 
[ Last edited by PG-13 on 2007-3-16 at 02:10 AM ] |   
 
 
 
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