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?

Pr (team 2 is not second)

= Pr (team 1 & team 2 are in the same half of draw)

= Pr (teams 1 & 2 are in top half OR teams 1 & 2 are in bottom half)

= (1/2 x 1/2) + (1/2 x 1/2)

= 1/2

Posted by David on 2004-07-07 01:29:55