Puzzles
A ballot count where the winner never trails
In an election, candidate A beats candidate B by a final tally of p votes to q votes (with p > q). If the ballots are drawn and counted one at a time in a completely random order, what's the probability that A stays strictly ahead of B for the entire count — never once tied, never once trailing?
Reveal the answer
The probability A leads the whole way through is (p − q) / (p + q). It's named after Joseph Bertrand, who published it in 1887 — though the Englishman W. A. Whitworth had actually proved the same result nine years earlier, in 1878, and it's Bertrand's version that stuck. The clean, widely-taught reflection-based proof came later still, from Désiré André. Not to be confused with Bertrand's other famous puzzle, the Box Paradox.