- 帖子
- 199
- 精華
- 0
- 威望
- 102
- 魅力
- 3
- 讚好
- 0
|
94#
發表於 2007-3-16 01:17 AM
| 只看該作者
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 ] |
|