Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge 2004 Paper 2 5 ii Solution Created 2026-10-18 Updated 2026-10-20
Each additional pair of independent shots resolves the tie with probability , since exactly one team must score. It preserves the tie with probability . Finishing after shots means an initial tie, then tied pairs, then a decisive pair. Independence and geometric continuation after an initial tie giveBecause , and . The total eventual winning probability is the sum of winning in the first ten shots and winning later:Equivalently, conditional on the initial tie, the probability of still being tied after further pairs is .