Probability :Knock Out Tournament Of Ranked Players 
Thirty-two players ranked 1 to 32 are playing in a knockout
  tournament. Assume that in every match between any two players, the
  better-ranked player wins, the probability that ranked 1 and ranked 2
  players are winner and runner up respectively, is ?

I dont understand. Should'nt the player ranked 1 always be the winner as the better ranked guy always wins?

If you picture the usual tree diagram for a tournament bracket, you'll see that the 1 and 2 seeds will meet in the final if and only if they start on opposite sides of the bracket.  By symmetry, it doesn't matter where you position the 1 seed (so you may as well place her say at the top left).  This leaves $31$ possible starting positions for the 2 seed, $16$ of which are on the opposite side from the 1 seed.  So the probability they'll meet in the final (where the 1 seed will prevail) is
$${16\over31}\approx.516129$$
