RE: Probability question: names in hats
March 18, 2016 at 1:44 am
(This post was last modified: March 18, 2016 at 6:45 am by Aractus.)
The probability tree I posted should be easy to follow as each line is drawn from the number selected. So the far left, the first choice represents a choice of any of the numbers 1-4, and if 4 is selected winning is impossible. If 1 is selected then person 1 needs to reselect hence "1b". The number 1 is returned after their selection (i.e. after 1b and where person 2 can chose from).
Here's an edited picture with the self-selected number returned to the Xb picks, if it makes it any clearer:
![[Image: 40FmIpH.png]](https://images.weserv.nl/?url=i.imgur.com%2F40FmIpH.png)
When playing the actual game you will keep playing beyond the losing positions, but they're already losing positions so there's no point in considering further possibilities for them as they're already at a losing point. You really need to go to 5 numbers to see the pattern properly though because as I mentioned for N players number N-1 can't be available past the N-2nd selection (i.e. if the 3rd selection is between 3 and 4 then player 3 must select 4 and return 3 to be selected by 4 in this example).
Here's an edited picture with the self-selected number returned to the Xb picks, if it makes it any clearer:
When playing the actual game you will keep playing beyond the losing positions, but they're already losing positions so there's no point in considering further possibilities for them as they're already at a losing point. You really need to go to 5 numbers to see the pattern properly though because as I mentioned for N players number N-1 can't be available past the N-2nd selection (i.e. if the 3rd selection is between 3 and 4 then player 3 must select 4 and return 3 to be selected by 4 in this example).
For Religion & Health see:[/b][/size] Williams & Sternthal. (2007). Spirituality, religion and health: Evidence and research directions. Med. J. Aust., 186(10), S47-S50. -LINK
The WIN/Gallup End of Year Survey 2013 found the US was perceived to be the greatest threat to world peace by a huge margin, with 24% of respondents fearful of the US followed by: 8% for Pakistan, and 6% for China. This was followed by 5% each for: Afghanistan, Iran, Israel, North Korea. -LINK
"That's disgusting. There were clean athletes out there that have had their whole careers ruined by people like Lance Armstrong who just bended thoughts to fit their circumstances. He didn't look up cheating because he wanted to stop, he wanted to justify what he was doing and to keep that continuing on." - Nicole Cooke
The WIN/Gallup End of Year Survey 2013 found the US was perceived to be the greatest threat to world peace by a huge margin, with 24% of respondents fearful of the US followed by: 8% for Pakistan, and 6% for China. This was followed by 5% each for: Afghanistan, Iran, Israel, North Korea. -LINK
"That's disgusting. There were clean athletes out there that have had their whole careers ruined by people like Lance Armstrong who just bended thoughts to fit their circumstances. He didn't look up cheating because he wanted to stop, he wanted to justify what he was doing and to keep that continuing on." - Nicole Cooke
