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
- The Handshake Count 3.0/10
- Eight Rooks 3.0/10
Source: Posed by Joseph Bertrand (1887); the reflection argument is due to Desire Andre (1887). Statement written for AxiomIQ.