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MathNet 2017-part-07 — 172 problems (EN–VI) Question 33

Math Olympiad Vault · MathNet 2017-part-07 — 172 problems (EN–VI)

Question 33

You have $128$ teams in a single elimination tournament. The Engineers and the Crimson are two of these teams. Each of the $128$ teams in the tournament is equally strong, so during each match, each team has an equal probability of winning.

Now, the $128$ teams are randomly put into the bracket.

What is the probability that the Engineers play the Crimson sometime during the tournament?