Puzzle of the Week #173 - Tournament

There are 16 teams in the knockout stages of a football tournament. For the sake of argument, say that each team has a distinct ranking from 1 (best) to 16 (worst), and that in any individual match, the better team will always win and progress to the next round.

The first round matches are randomly arranged, and the eight winners of those matches are randomly arranged in four matches in the quarter final etc.

Which of the following scenarios is more likely:

The 2nd ranked team is knocked out before the semi-finals, or

The 7th ranked team progresses at least as far as the semi-finals?