TL;DR
Catalan Numbers and Ballot Sequences: A canonical quantitative trading interview question at olympiad difficulty. Commonly asked at Jane Street, HRT, Two Sigma.
By Valenke Exam Prep Team·Last updated 2026-06-01
olympiadCombinatorial Arguments
Catalan Numbers and Ballot Sequences
Asked at: Jane Street, HRT, Two Sigma
Problem
In an election, candidate A receives votes and candidate B receives votes. Votes are counted one at a time. What is the probability that A is strictly ahead throughout the entire counting (never tied or behind after the first vote)? Express the answer in terms of the Catalan numbers.
Related concepts
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