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Game of luck (Posted on 2004-01-27) Difficulty: 2 of 5
4 people play a game of chance. They each take turns until everyone has taken a turn, then they begin a new round. They stay in the same order every round. Every time a player takes a turn, they have a certain chance of winning. When someone wins, the game ends. They all have even odds of winning a game. The chance of someone winning in any given round is 3/5.

What is the probability for each person to win during their turns?

  Submitted by Tristan    
Rating: 3.4000 (5 votes)
Solution: (Hide)
The probabilities are: 3/20 for the first player, 3/17 for the second, 3/14 for the third, and 3/11 for the last.

Since the chance of anyone winning in a round is 3/5 and they all have even chances of winning, they must each have 3/20 chance of winning in a round. The players who donít go first, however, have a chance that they may not get to take their turns at all. So, the players who donít go first actually have a better chance to win during their turns, provided that their turns come.

You divide the chance of winning by the chance of getting a turn, and you get the chance of winning during the turn.
2nd player: (3/20)/(17/20)=3/17
3rd player: (3/20)/(14/20)=3/14
4th player: (3/20)/(11/20)=3/11

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: Clarification =happy endingAdy TZIDON2004-02-04 15:14:30
Hints/TipsClarificationTristan2004-02-03 20:12:43
re(6): another remark to SK 'S solutionCharlie2004-02-01 12:06:36
re(6): another remark to SK 'S solutionSilverKnight2004-01-31 18:54:46
Some Thoughtsre(5): another remark to SK 'S solutionAdy TZIDON2004-01-31 17:51:41
re(4): another remark to SK 'S solutionCharlie2004-01-31 14:09:22
Some Thoughtsre(3): another remark to SK 'S solutionAdy TZIDON2004-01-31 13:02:39
re(2): another remark to SK 'S solutionCharlie2004-01-31 11:53:51
re: another remark to SK 'S solutionCharlie2004-01-31 11:50:33
another remark to SK 'S solutionAdy TZIDON2004-01-31 10:37:38
re(2): my solutionAdy TZIDON2004-01-31 10:21:39
re: my solutionSilverKnight2004-01-30 14:08:05
Solutionmy solutionAdy TZIDON2004-01-30 11:54:53
QuestionQuestionPenny2004-01-27 18:45:07
re(2): Charlie's solutionCharlie2004-01-27 14:19:19
re(2): Charlie's solutionSilverKnight2004-01-27 14:18:27
re: Charlie's solutionSilverKnight2004-01-27 14:17:11
Solutionre: solution -- on second thoughtCharlie2004-01-27 14:14:29
SolutionsolutionSilverKnight2004-01-27 14:04:28
solutionBrian Smith2004-01-27 13:56:34
SolutionsolutionCharlie2004-01-27 13:41:23
No SubjectVictor Zapana2004-01-27 13:15:47
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