Solution
The Ballot Problem
Show the problem again
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.
Worked solution
The answer is 1/5. By the Ballot Theorem, if A receives a votes and B receives b votes with a > b, the probability that A leads strictly throughout counting is (a − b)/(a + b). Here (60 − 40)/(60 + 40) = 20/100 = 1/5.
Source: Posed by Joseph Bertrand (1887); the reflection argument is due to Desire Andre (1887). Statement written for AxiomIQ.