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The Tournament (Posted on 2004-06-15) Difficulty: 2 of 5
In a basketball tournament, there are teams named 1 through 8, such that a lower number team is better than a higher numbered team. (1 is best, 2 is second best... 8 is worst) Also, a better team will always win over a worse team. (There are no upsets)

?-\__
?-/  |
     |--\
?-\__|  |
?-/     |
        |-WINNER
?-\__   |
?-/  |  |
     |--/
?-\__|
?-/
Here is the grid for the tournament

If the better team always wins (there are no upsets) and if the pairing is completely random, what is the easiest way to figure the probability that team 2 doesn't win second place?

  Submitted by Gamer    
Rating: 2.4000 (5 votes)
Solution: (Hide)
Since the pairing is symmetric, put 1 in any spot. There are 3 spots where 1 will play 2 before the last branch, and 4 places where 2 will not. Because the only way 2 won't win second place is if it plays 1 before the last branch, the probability is 3/7.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No SubjectArthur Swanson2022-12-12 04:09:37
AmazingNick Williams2004-07-21 20:09:07
SolutionMay be like this...Strahinja2004-07-10 05:18:16
SolutionNo SubjectDavid2004-07-07 01:29:55
easy...Strahinja2004-07-02 09:28:23
The Answer is Easy...seant2004-06-18 20:40:56
just a guesskristi2004-06-18 00:56:10
re: this is easyCharlie2004-06-15 13:02:49
Solutionthis is easynate2004-06-15 12:58:01
Solutionre: So why not do it the hard way? WHY NOT EVEN HARDERAdy TZIDON2004-06-15 12:05:18
SolutionSo why not do it the hard way?Jer2004-06-15 09:09:21
SolutionSimplee.g.2004-06-15 07:59:06
ELEMENTARY, DEAR WATSONAdy TZIDON2004-06-15 06:11:39
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