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 The Tournament (Posted on 2004-06-15)
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.

 Subject Author Date Amazing Nick Williams 2004-07-21 20:09:07 May be like this... Strahinja 2004-07-10 05:18:16 No Subject David 2004-07-07 01:29:55 easy... Strahinja 2004-07-02 09:28:23 The Answer is Easy... seant 2004-06-18 20:40:56 just a guess kristi 2004-06-18 00:56:10 re: this is easy Charlie 2004-06-15 13:02:49 this is easy nate 2004-06-15 12:58:01 re: So why not do it the hard way? WHY NOT EVEN HARDER Ady TZIDON 2004-06-15 12:05:18 So why not do it the hard way? Jer 2004-06-15 09:09:21 Simple e.g. 2004-06-15 07:59:06 ELEMENTARY, DEAR WATSON Ady TZIDON 2004-06-15 06:11:39

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