medium Probability
A release-checked medium problem for training Combinations and Permutations, Conditional Probability, Events, Combinatorics.
A single-elimination poker tournament has $2^n$ players, each with a distinct rating. In each match, the higher rated opponent always wins against the lower rated opponent, and that the winner proceeds to the subsequent round. What is the probability that the highest rated and second-highest rated players will meet in the final? Solve this for when $n = 10$.
This Probability problem is tagged Combinations and Permutations, Conditional Probability, Events, Combinatorics. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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