Which team holds the top score?

Question

Team X has 4 players and Team Y has 6 players. All 10 players post independent scores from the same continuous distribution, so no two scores tie.

What is the probability that the single highest score belongs to a Team Y player?

Accepted Answer

Pool all 10 scores. They are exchangeable, so each is equally likely to be the highest. Team Y owns 6 of the 10 scores, so the top score is theirs with probability equal to their share: \frac{6}{10} = \frac{3}{5} = 0.6. Takeaway. The overall maximum lands in a group with probability equal to that group's fraction of the pool.

Which team holds the top score?

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