In a tennis tournement of 128 players, elimination system, what is the probability that two twins will meet at some point?

probability probability-theory

Assuming everyone's of equal skill and there's uniformly random initial seeding, we can appeal to symmetry:

Suppose there are $2^n$ players.

There are $2^n(2^n-1)/2$ pairs of players.

There are $2^n-1$ matches.

Therefore the probability they meet is $$\frac{1}{2^{n-1}}$$


Hint: What is the probability they need to win $i$ games each to play each other? If they need to win $i$ games each to play each other what is the probability it happens?

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