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Quit While You're Ahead (Posted on 2003-11-10) Difficulty: 2 of 5
Two men are playing Russian roulette using a pistol with six chambers.
A single bullet is used and the chamber is spun after every turn.

What is the probability that the first man will lose?

  Submitted by DJ    
Rating: 3.5556 (9 votes)
Solution: (Hide)
6/11

There is a 1/6 chance that he will lose on the first shot, and a 5/6 chance that he doesn't.
If he doesn't, the other man then also has a 1/6 chance (since the chamber is respun) of losing, and a 5/6 chance that he survives the second turn.
Therefore, there is a (5/6)(5/6)= 25/36 probability that the first man takes a second shot, at which point the game essentially starts over.

From this point, there is the same chance that he loses any time after the first shot as after the third shot, etc. Putting this into an equation:

P = 1/6 + (25/36)P
(11/36)P = 1/6
P = 6/11

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2008-04-14 16:24:41
AnswerK Sengupta2008-03-20 09:42:59
re(3): A footnote to this problemHal90002003-11-15 10:58:40
re(2): A footnote to this problemDan2003-11-13 09:54:00
No SubjectHal90002003-11-11 16:17:39
re(4): Inconclusive :-)Hal90002003-11-11 16:05:07
re(4): Inconclusive :-)SilverKnight2003-11-11 15:22:37
re(3): Inconclusive :-)SilverKnight2003-11-11 15:08:15
re(2): Inconclusive :-)Hal90002003-11-11 15:00:03
re: Inconclusive :-)SilverKnight2003-11-11 14:45:04
InconclusiveHal90002003-11-11 14:36:21
Some Thoughtsre(3): A footnote to this problemFederico Kereki2003-11-11 09:32:33
re(3): A footnote to this problemPopstar Dave2003-11-11 07:11:29
re(2): A footnote to this problemDan2003-11-10 20:30:57
Some Thoughtsre: A footnote to this problemPopstar Dave2003-11-10 18:50:30
A footnote to this problemDan2003-11-10 15:59:16
SolutionAn easy solutionFederico Kereki2003-11-10 12:46:22
completenessLee2003-11-10 11:45:12
re: solutionwonshot2003-11-10 10:32:29
solutionLee2003-11-10 10:29:36
re: Solutionwonshot2003-11-10 10:28:12
solutionwonshot2003-11-10 10:25:44
SolutionSolutionPopstar Dave2003-11-10 07:08:00
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