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Combinatorics 4.5/10

The Ballot Problem

In an election, Candidate A receives 60 votes and Candidate B receives 40 votes. Ballots are counted in a uniformly random order. What is the probability that Candidate A is strictly ahead of Candidate B throughout the entire counting process? Express as a fraction.

Related problems & prerequisites

Worth solving first

Source: Posed by Joseph Bertrand (1887); the reflection argument is due to Desire Andre (1887). Statement written for AxiomIQ.