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 Quit While You're Ahead (Posted on 2003-11-10)
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

 Subject Author Date Puzzle Solution K Sengupta 2008-04-14 16:24:41 Answer K Sengupta 2008-03-20 09:42:59 re(3): A footnote to this problem Hal9000 2003-11-15 10:58:40 re(2): A footnote to this problem Dan 2003-11-13 09:54:00 No Subject Hal9000 2003-11-11 16:17:39 re(4): Inconclusive :-) Hal9000 2003-11-11 16:05:07 re(4): Inconclusive :-) SilverKnight 2003-11-11 15:22:37 re(3): Inconclusive :-) SilverKnight 2003-11-11 15:08:15 re(2): Inconclusive :-) Hal9000 2003-11-11 15:00:03 re: Inconclusive :-) SilverKnight 2003-11-11 14:45:04 Inconclusive Hal9000 2003-11-11 14:36:21 re(3): A footnote to this problem Federico Kereki 2003-11-11 09:32:33 re(3): A footnote to this problem Popstar Dave 2003-11-11 07:11:29 re(2): A footnote to this problem Dan 2003-11-10 20:30:57 re: A footnote to this problem Popstar Dave 2003-11-10 18:50:30 A footnote to this problem Dan 2003-11-10 15:59:16 An easy solution Federico Kereki 2003-11-10 12:46:22 completeness Lee 2003-11-10 11:45:12 re: solution wonshot 2003-11-10 10:32:29 solution Lee 2003-11-10 10:29:36 re: Solution wonshot 2003-11-10 10:28:12 solution wonshot 2003-11-10 10:25:44 Solution Popstar Dave 2003-11-10 07:08:00

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