World Cup Champions

What this tournament-bracket probability question tests

This is a medium-difficulty probability question that tests your ability to reason about conditional outcomes in a structured elimination format. Rather than computing raw probabilities, the question requires you to think carefully about the path each team must take through the bracket to meet in the final, and how random seeding affects those paths.

The key insight is recognizing that two specific teams will meet in the final only if they are placed in opposite halves of the bracket and each wins all games on their side. Since higher-ranked teams always win, the challenge is purely combinatorial: counting the favorable bracket configurations relative to all possible random seedings. Interviewers use questions like this to see whether you can decompose a multi-stage problem into independent events and combine their probabilities correctly.

• Bracket structure and symmetry
• Path-dependent probability in elimination tournaments
• Conditional probability and independent events
• Combinatorial counting under constraints