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?

team 2 will not win second place if another team does.

The probabilities for the other teams to win second:

Team 3 needs 2 to be in the same as 1 and 3 to be in the other: 3/7*4/6 = 2/7

Team 4 needs 3 and 2 to be in the same as 1 and 4 to be in the other:  3/7*2/6*4/5 = 4/35

Team 5 needs 4, 3, and 2 to be in the same as 1:  3/7*2/6*1/5 = 1/35

Teams 6, 7 and 8 cannot make it to the final game.

So the solution, since 2 not make it if another team does: 

2/7 + 4/35 + 1/35 = 3/7

-Jer

Posted by Jer on 2004-06-15 09:09:21